initial commit
This commit is contained in:
1
.direnv/flake-profile
Symbolic link
1
.direnv/flake-profile
Symbolic link
@@ -0,0 +1 @@
|
|||||||
|
flake-profile-2-link
|
||||||
1
.direnv/flake-profile-2-link
Symbolic link
1
.direnv/flake-profile-2-link
Symbolic link
@@ -0,0 +1 @@
|
|||||||
|
/nix/store/99fjzvv2y3g37jbqi28q8080db1183xk-latex-env
|
||||||
7
Assignment4_211.aux
Normal file
7
Assignment4_211.aux
Normal file
@@ -0,0 +1,7 @@
|
|||||||
|
\relax
|
||||||
|
\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
|
||||||
|
\@nameuse{bbl@beforestart}
|
||||||
|
\catcode `"\active
|
||||||
|
\babel@aux{english}{}
|
||||||
|
\babel@aux{austrian}{}
|
||||||
|
\gdef \@abspage@last{6}
|
||||||
91
Assignment4_211.fdb_latexmk
Normal file
91
Assignment4_211.fdb_latexmk
Normal file
@@ -0,0 +1,91 @@
|
|||||||
|
# Fdb version 4
|
||||||
|
["pdflatex"] 1780937132.21957 "Assignment4_211.tex" "Assignment4_211.pdf" "Assignment4_211" 1780937132.89663 0
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/map/fontname/texfonts.map" 1 3524 cb3e574dea2d1052e39280babc910dc8 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1 1004 54797486969f23fa377b128694d548df ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1 916 f87d7c45f9c908e672703b83b72241a3 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msam7.tfm" 1 928 2dc8d444221b7a635bb58038579b861a ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1 908 2921f8a10601f252058503cc6570e581 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1 940 228d6584342e91276bf566bcf9716b83 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmbx12.tfm" 1 1324 c910af8c371558dc20f2d7822f66fe64 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmex10.tfm" 1 992 662f679a0b3d2d53c1b94050fdaa3f50 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi12.tfm" 1 1524 4414a8315f39513458b80dfc63bff03a ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi6.tfm" 1 1512 f21f83efb36853c0b70002322c1ab3ad ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi8.tfm" 1 1520 eccf95517727cb11801f4f1aee3a21b4 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr12.tfm" 1 1288 655e228510b4c2a1abe905c368440826 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr6.tfm" 1 1300 b62933e007d01cfd073f79b963c01526 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr8.tfm" 1 1292 21c1c5bfeaebccffdb478fd231a0997d ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmss12.tfm" 1 1324 37b971caf729d7edd9cbb9f9b0ea76eb ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmssbx10.tfm" 1 1272 e2d13f0df30bf3ad990bb9d028e37f34 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmssi12.tfm" 1 1532 48589e216c7fb787d0f3ee1a3047705d ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy10.tfm" 1 1124 6c73e740cf17375f03eec0ee63599741 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy6.tfm" 1 1116 933a60c408fc0a863a92debe84b2d294 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy8.tfm" 1 1120 8b7d695260f3cff42e636090a8002094 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1 32080 340ef9bf63678554ee606688e7b5339d ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1 30251 6afa5cb1d0204815a708a080681d4674 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi12.pfb" 1 36741 fa121aac0049305630cf160b86157ee4 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi6.pfb" 1 37166 8ab3487cbe3ab49ebce74c29ea2418db ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi8.pfb" 1 35469 70d41d2b9ea31d5d813066df7c99281c ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1 32722 d7379af29a190c3f453aba36302ff5a9 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssbx10.pfb" 1 28902 2f5c04fd2884d1878057baa5aad22765 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssi12.pfb" 1 25095 0ff1f6d531b320ecbbd6ea84d875816c ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1 32569 5e5ddc8df908dea60932f3c484a54c0d ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/context/base/mkii/supp-pdf.mkii" 1 71627 94eb9990bed73c364d7f53f960cc8c5b ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-english/english.ldf" 1 7008 9ff5fdcc865b01beca2b0fe4a46231d4 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/austrian.ldf" 1 2238 5a1f6203e82197c5a4435155488ffdcf ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/babel-german.def" 1 32946 cb91c8893d96faf3f2fd433dbf43f3f1 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/babel.sty" 1 147019 f2ca437186bfeb562e1066ad59426a04 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-austrian.tex" 1 670 ed2363bc8191e44da866315c2a7eb96c ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-de-AT-1901.ini" 1 4996 a7449054008fbf7583054d19176ec406 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-en.ini" 1 3936 fef897bbcfe8e9d18c93a3d2d53cf9d8 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-english.tex" 1 374 a9c05f002d9437e6de45ac1cc23d56c2 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/txtbabel.def" 1 5231 c1599e5bf7d2ee42743212a7f8d20a56 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/iftex/iftex.sty" 1 7984 7dbb9280f03c0a315425f1b4f35d43ee ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/infwarerr/infwarerr.sty" 1 8356 7bbb2c2373aa810be568c29e333da8ed ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/kvdefinekeys/kvdefinekeys.sty" 1 5412 d5a2436094cd7be85769db90f29250a6 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/ltxcmds/ltxcmds.sty" 1 17865 1a9bd36b4f98178fa551aca822290953 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/pdftexcmds/pdftexcmds.sty" 1 20089 80423eac55aa175305d35b49e04fe23b ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amsfonts.sty" 1 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amssymb.sty" 1 13829 94730e64147574077f8ecfea9bb69af4 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsa.fd" 1 961 6518c6525a34feb5e8250ffa91731cff ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsb.fd" 1 961 d02606146ba5601b5645f987c92e6193 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsbsy.sty" 1 2222 27db7d52163edae53881b71ff62e754e ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsgen.sty" 1 4173 1b3e76addfb8afcb47db4811d66e1dc6 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsmath.sty" 1 88471 b1bb09142edddebd46ba986341b867bd ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsopn.sty" 1 4474 c510a88aa5f51b8c773b50a7ee92befd ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amstext.sty" 1 2444 9983e1d0683f102e3b190c64a49313aa ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/article.cls" 1 20144 b966087dda3b194755eb460d32e2ef75 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/inputenc.sty" 1 5048 0270515b828149155424600fd2d58ac5 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/size12.clo" 1 8449 8dc66c6c313c8eb2d774af83bca435dd ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1 13886 d1306dcf79a944f6988e688c1785f9ce ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf.sty" 1 4393 47f27fd4d95928d20b1885ba77de11d2 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-cfg/graphics.cfg" 1 1224 978390e9c2234eab29404bc21b268d1e ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-def/pdftex.def" 1 19626 23e2822b9b2b5005f4c549ca98b9334d ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphics.sty" 1 18363 69bb4f5538964bfea50d1e6d89cbe69f ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphicx.sty" 1 8118 43b99e52946c33a23f5f43b52d5cc5ec ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/keyval.sty" 1 2671 d9941f4bf4750e9b0603c9a2ec54693b ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/trig.sty" 1 4023 e66acf578d6b564c4670fb57ff336a7a ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/grfext/grfext.sty" 1 7133 b94bbacbee6e4fdccdc7f810b2aec370 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvoptions/kvoptions.sty" 1 22555 6d8e155cfef6d82c3d5c742fea7c992e ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvsetkeys/kvsetkeys.sty" 1 13815 760b0c02f691ea230f5359c4e1de23a7 ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/l3backend/l3backend-pdftex.def" 1 30662 bfd6e864f4ffc5018b0e2b6260c3181c ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg" 1 678 4792914a8f45be57bb98413425e4c7af ""
|
||||||
|
"/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/multirow/multirow.sty" 1 6696 886c9f3087d0b973ed2c19aa79cb3023 ""
|
||||||
|
"/nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1 5541489 98dcaa26546008c59b74ed5f7e93078c ""
|
||||||
|
"/nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/web2c/pdftex/pdflatex.fmt" 1 3637270 2f5a0a831f2ff9f2929d06d36e122866 ""
|
||||||
|
"/nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/web2c/texmf.cnf" 1 44263 cffdb522e8ff03abb028d8b9b1d3dcaf ""
|
||||||
|
"Assignment4_211.aux" 1780937132.85779 193 347950d4fe37faf4cda436926310d6c9 "pdflatex"
|
||||||
|
"Assignment4_211.tex" 1780937131.07975 7340 5eda71aa5204acd3ada880aeb21beff0 ""
|
||||||
|
"fig/fig1.1.png" 1780661010.16298 29540 fbe16c23e73dd5b574352e19d95cefab ""
|
||||||
|
"fig/fig1.2.png" 1780661025.82539 23905 f6bafcade54f5f0c79bd69f01e99ef22 ""
|
||||||
|
"fig/fig1.3.png" 1780661037.90572 103888 fc80510949e033cc1ea8097918da30c8 ""
|
||||||
|
"fig/fig1.4.png" 1780664950.44617 50673 8282f7d7a9a6bbb198f3f8088612d58d ""
|
||||||
|
"fig/fig3.1.png" 1780666655.93179 362615 411378ab0ed29697877a5e0d95a522f0 ""
|
||||||
|
"fig/fig4.1.png" 1780672164.80068 31524 5546400b68ed83ec746009978f8e732a ""
|
||||||
|
"fig/fig4.2.png" 1780672272.76268 29167 847b86c140a9ad57ffea3fee13be55d0 ""
|
||||||
|
(generated)
|
||||||
|
"Assignment4_211.aux"
|
||||||
|
"Assignment4_211.log"
|
||||||
|
"Assignment4_211.pdf"
|
||||||
|
(rewritten before read)
|
||||||
172
Assignment4_211.fls
Normal file
172
Assignment4_211.fls
Normal file
@@ -0,0 +1,172 @@
|
|||||||
|
PWD /home/quirinecker/projects/semester06-signal_processing/assignment04
|
||||||
|
INPUT /nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/web2c/texmf.cnf
|
||||||
|
INPUT /nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/web2c/pdftex/pdflatex.fmt
|
||||||
|
INPUT Assignment4_211.tex
|
||||||
|
OUTPUT Assignment4_211.log
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/article.cls
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/article.cls
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/size12.clo
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/size12.clo
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/size12.clo
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/map/fontname/texfonts.map
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphicx.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphicx.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/keyval.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/keyval.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphics.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphics.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/trig.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/trig.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-cfg/graphics.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-cfg/graphics.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-cfg/graphics.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-def/pdftex.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-def/pdftex.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-def/pdftex.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/babel.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/babel.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/txtbabel.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-austrian.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-austrian.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-austrian.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-english.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-english.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-english.tex
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-de-AT-1901.ini
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/austrian.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/austrian.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/austrian.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/babel-german.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-en.ini
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-english/english.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-english/english.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-english/english.ldf
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/inputenc.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/inputenc.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/multirow/multirow.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/multirow/multirow.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/infwarerr/infwarerr.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/infwarerr/infwarerr.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/grfext/grfext.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/grfext/grfext.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/kvdefinekeys/kvdefinekeys.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/kvdefinekeys/kvdefinekeys.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvoptions/kvoptions.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvoptions/kvoptions.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/ltxcmds/ltxcmds.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/ltxcmds/ltxcmds.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvsetkeys/kvsetkeys.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvsetkeys/kvsetkeys.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/pdftexcmds/pdftexcmds.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/pdftexcmds/pdftexcmds.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/iftex/iftex.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/iftex/iftex.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf-base.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf-base.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsmath.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsmath.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsopn.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amstext.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amstext.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsgen.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsgen.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsbsy.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsbsy.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsopn.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amssymb.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amssymb.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amsfonts.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amsfonts.sty
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/l3backend/l3backend-pdftex.def
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/l3backend/l3backend-pdftex.def
|
||||||
|
INPUT ./Assignment4_211.aux
|
||||||
|
INPUT ./Assignment4_211.aux
|
||||||
|
INPUT Assignment4_211.aux
|
||||||
|
OUTPUT Assignment4_211.aux
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/context/base/mkii/supp-pdf.mkii
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/context/base/mkii/supp-pdf.mkii
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/context/base/mkii/supp-pdf.mkii
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmbx12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmbx12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmbx12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmss12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmssbx10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmssi12.tfm
|
||||||
|
INPUT ./fig/fig1.1.png
|
||||||
|
INPUT ./fig/fig1.1.png
|
||||||
|
INPUT ./fig/fig1.1.png
|
||||||
|
INPUT ./fig/fig1.1.png
|
||||||
|
OUTPUT Assignment4_211.pdf
|
||||||
|
INPUT ./fig/fig1.1.png
|
||||||
|
INPUT ./fig/fig1.2.png
|
||||||
|
INPUT ./fig/fig1.2.png
|
||||||
|
INPUT ./fig/fig1.2.png
|
||||||
|
INPUT ./fig/fig1.2.png
|
||||||
|
INPUT ./fig/fig1.2.png
|
||||||
|
INPUT /nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr8.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmr6.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi12.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi8.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmmi6.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy8.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmsy6.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/cm/cmex10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsa.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsa.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsa.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsb.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsb.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsb.fd
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
|
||||||
|
INPUT ./fig/fig1.3.png
|
||||||
|
INPUT ./fig/fig1.3.png
|
||||||
|
INPUT ./fig/fig1.3.png
|
||||||
|
INPUT ./fig/fig1.3.png
|
||||||
|
INPUT ./fig/fig1.3.png
|
||||||
|
INPUT ./fig/fig1.4.png
|
||||||
|
INPUT ./fig/fig1.4.png
|
||||||
|
INPUT ./fig/fig1.4.png
|
||||||
|
INPUT ./fig/fig1.4.png
|
||||||
|
INPUT ./fig/fig1.4.png
|
||||||
|
INPUT ./fig/fig3.1.png
|
||||||
|
INPUT ./fig/fig3.1.png
|
||||||
|
INPUT ./fig/fig3.1.png
|
||||||
|
INPUT ./fig/fig3.1.png
|
||||||
|
INPUT ./fig/fig3.1.png
|
||||||
|
INPUT ./fig/fig4.1.png
|
||||||
|
INPUT ./fig/fig4.1.png
|
||||||
|
INPUT ./fig/fig4.1.png
|
||||||
|
INPUT ./fig/fig4.1.png
|
||||||
|
INPUT ./fig/fig4.1.png
|
||||||
|
INPUT ./fig/fig4.2.png
|
||||||
|
INPUT ./fig/fig4.2.png
|
||||||
|
INPUT ./fig/fig4.2.png
|
||||||
|
INPUT ./fig/fig4.2.png
|
||||||
|
INPUT ./fig/fig4.2.png
|
||||||
|
INPUT Assignment4_211.aux
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmex10.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi12.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi6.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi8.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr12.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr8.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssbx10.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssi12.pfb
|
||||||
|
INPUT /nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
|
||||||
348
Assignment4_211.log
Normal file
348
Assignment4_211.log
Normal file
@@ -0,0 +1,348 @@
|
|||||||
|
This is pdfTeX, Version 3.141592653-2.6-1.40.27 (TeX Live 2025/nixos.org) (preloaded format=pdflatex 1980.1.1) 8 JUN 2026 18:45
|
||||||
|
entering extended mode
|
||||||
|
restricted \write18 enabled.
|
||||||
|
file:line:error style messages enabled.
|
||||||
|
%&-line parsing enabled.
|
||||||
|
**Assignment4_211.tex
|
||||||
|
(./Assignment4_211.tex
|
||||||
|
LaTeX2e <2025-11-01>
|
||||||
|
L3 programming layer <2026-01-19>
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/article.cls
|
||||||
|
Document Class: article 2025/01/22 v1.4n Standard LaTeX document class
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/size12.clo
|
||||||
|
File: size12.clo 2025/01/22 v1.4n Standard LaTeX file (size option)
|
||||||
|
)
|
||||||
|
\c@part=\count275
|
||||||
|
\c@section=\count276
|
||||||
|
\c@subsection=\count277
|
||||||
|
\c@subsubsection=\count278
|
||||||
|
\c@paragraph=\count279
|
||||||
|
\c@subparagraph=\count280
|
||||||
|
\c@figure=\count281
|
||||||
|
\c@table=\count282
|
||||||
|
\abovecaptionskip=\skip49
|
||||||
|
\belowcaptionskip=\skip50
|
||||||
|
\bibindent=\dimen148
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphicx.sty
|
||||||
|
Package: graphicx 2024/12/31 v1.2e Enhanced LaTeX Graphics (DPC,SPQR)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/keyval.sty
|
||||||
|
Package: keyval 2022/05/29 v1.15 key=value parser (DPC)
|
||||||
|
\KV@toks@=\toks17
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/graphics.sty
|
||||||
|
Package: graphics 2024/08/06 v1.4g Standard LaTeX Graphics (DPC,SPQR)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics/trig.sty
|
||||||
|
Package: trig 2023/12/02 v1.11 sin cos tan (DPC)
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-cfg/graphics.cfg
|
||||||
|
File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
|
||||||
|
)
|
||||||
|
Package graphics Info: Driver file: pdftex.def on input line 106.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/graphics-def/pdftex.def
|
||||||
|
File: pdftex.def 2025/09/29 v1.2d Graphics/color driver for pdftex
|
||||||
|
))
|
||||||
|
\Gin@req@height=\dimen149
|
||||||
|
\Gin@req@width=\dimen150
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/babel.sty
|
||||||
|
Package: babel 2026/02/14 v26.3 The multilingual framework for LuaLaTeX, pdfLaTeX and XeLaTeX
|
||||||
|
\babel@savecnt=\count283
|
||||||
|
LaTeX Encoding Info: Redeclaring text command \ij (encoding OT1) on input line 2078.
|
||||||
|
LaTeX Encoding Info: Redeclaring text command \IJ (encoding OT1) on input line 2080.
|
||||||
|
LaTeX Encoding Info: Redeclaring text command \ij (encoding T1) on input line 2082.
|
||||||
|
LaTeX Encoding Info: Redeclaring text command \IJ (encoding T1) on input line 2083.
|
||||||
|
LaTeX Encoding Info: Ignoring declaration for text command \ij (encoding ?) on input line 2084.
|
||||||
|
LaTeX Encoding Info: Ignoring declaration for text command \IJ (encoding ?) on input line 2086.
|
||||||
|
LaTeX Encoding Info: Ignoring declaration for text command \SS (encoding ?) on input line 2111.
|
||||||
|
\U@D=\dimen151
|
||||||
|
\l@unhyphenated=\language90
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/txtbabel.def)
|
||||||
|
\bbl@readstream=\read2
|
||||||
|
\bbl@dirlevel=\count284
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/de/babel-austrian.tex) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel/locale/en/babel-english.tex)
|
||||||
|
|
||||||
|
Package babel Warning: The name 'austrian' with the 'ldf' mechanism is
|
||||||
|
(babel) assigned to the old 1901 variant of Austrian German.
|
||||||
|
(babel) For modern Austrian German, use the name 'naustrian'.
|
||||||
|
(babel) Reported on input line 4330.
|
||||||
|
|
||||||
|
Package babel Info: Importing font and identification data for austrian
|
||||||
|
(babel) from babel-de-AT-1901.ini. Reported on input line 4330.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/austrian.ldf
|
||||||
|
Language: austrian
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-german/babel-german.def
|
||||||
|
Package babel Info: Hyphen rules for 'austrian' set to \l@german
|
||||||
|
(babel) (\language34). Reported on input line 178.
|
||||||
|
Package babel Info: Making " an active character on input line 470.
|
||||||
|
))
|
||||||
|
Package babel Info: Importing font and identification data for english
|
||||||
|
(babel) from babel-en.ini. Reported on input line 4330.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/babel-english/english.ldf
|
||||||
|
Language: english 2017/06/06 v3.3r English support from the babel system
|
||||||
|
Package babel Info: Hyphen rules for 'canadian' set to \l@english
|
||||||
|
(babel) (\language0). Reported on input line 102.
|
||||||
|
Package babel Info: Hyphen rules for 'australian' set to \l@ukenglish
|
||||||
|
(babel) (\language22). Reported on input line 105.
|
||||||
|
Package babel Info: Hyphen rules for 'newzealand' set to \l@ukenglish
|
||||||
|
(babel) (\language22). Reported on input line 108.
|
||||||
|
)) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/base/inputenc.sty
|
||||||
|
Package: inputenc 2024/02/08 v1.3d Input encoding file
|
||||||
|
\inpenc@prehook=\toks18
|
||||||
|
\inpenc@posthook=\toks19
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/multirow/multirow.sty
|
||||||
|
Package: multirow 2024/11/12 v2.9 Span multiple rows of a table
|
||||||
|
\multirow@colwidth=\skip51
|
||||||
|
\multirow@cntb=\count285
|
||||||
|
\multirow@dima=\skip52
|
||||||
|
\bigstrutjot=\dimen152
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf.sty
|
||||||
|
Package: epstopdf 2020-01-24 v2.11 Conversion with epstopdf on the fly (HO)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/infwarerr/infwarerr.sty
|
||||||
|
Package: infwarerr 2019/12/03 v1.5 Providing info/warning/error messages (HO)
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/grfext/grfext.sty
|
||||||
|
Package: grfext 2019/12/03 v1.3 Manage graphics extensions (HO)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/kvdefinekeys/kvdefinekeys.sty
|
||||||
|
Package: kvdefinekeys 2019-12-19 v1.6 Define keys (HO)
|
||||||
|
)) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvoptions/kvoptions.sty
|
||||||
|
Package: kvoptions 2022-06-15 v3.15 Key value format for package options (HO)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/ltxcmds/ltxcmds.sty
|
||||||
|
Package: ltxcmds 2023-12-04 v1.26 LaTeX kernel commands for general use (HO)
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/kvsetkeys/kvsetkeys.sty
|
||||||
|
Package: kvsetkeys 2022-10-05 v1.19 Key value parser (HO)
|
||||||
|
)) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/pdftexcmds/pdftexcmds.sty
|
||||||
|
Package: pdftexcmds 2020-06-27 v0.33 Utility functions of pdfTeX for LuaTeX (HO)
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/generic/iftex/iftex.sty
|
||||||
|
Package: iftex 2024/12/12 v1.0g TeX engine tests
|
||||||
|
)
|
||||||
|
Package pdftexcmds Info: \pdf@primitive is available.
|
||||||
|
Package pdftexcmds Info: \pdf@ifprimitive is available.
|
||||||
|
Package pdftexcmds Info: \pdfdraftmode found.
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/epstopdf-pkg/epstopdf-base.sty
|
||||||
|
Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
|
||||||
|
Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 485.
|
||||||
|
Package grfext Info: Graphics extension search list:
|
||||||
|
(grfext) [.pdf,.png,.jpg,.mps,.jpeg,.jbig2,.jb2,.PDF,.PNG,.JPG,.JPEG,.JBIG2,.JB2,.eps]
|
||||||
|
(grfext) \AppendGraphicsExtensions on input line 504.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||||
|
File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
|
||||||
|
)))
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsmath.sty
|
||||||
|
Package: amsmath 2025/07/09 v2.17z AMS math features
|
||||||
|
\@mathmargin=\skip53
|
||||||
|
|
||||||
|
For additional information on amsmath, use the `?' option.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amstext.sty
|
||||||
|
Package: amstext 2024/11/17 v2.01 AMS text
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsgen.sty
|
||||||
|
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||||
|
\@emptytoks=\toks20
|
||||||
|
\ex@=\dimen153
|
||||||
|
)) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsbsy.sty
|
||||||
|
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||||
|
\pmbraise@=\dimen154
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsmath/amsopn.sty
|
||||||
|
Package: amsopn 2022/04/08 v2.04 operator names
|
||||||
|
)
|
||||||
|
\inf@bad=\count286
|
||||||
|
LaTeX Info: Redefining \frac on input line 233.
|
||||||
|
\uproot@=\count287
|
||||||
|
\leftroot@=\count288
|
||||||
|
LaTeX Info: Redefining \overline on input line 398.
|
||||||
|
LaTeX Info: Redefining \colon on input line 409.
|
||||||
|
\classnum@=\count289
|
||||||
|
\DOTSCASE@=\count290
|
||||||
|
LaTeX Info: Redefining \ldots on input line 495.
|
||||||
|
LaTeX Info: Redefining \dots on input line 498.
|
||||||
|
LaTeX Info: Redefining \cdots on input line 619.
|
||||||
|
\Mathstrutbox@=\box53
|
||||||
|
\strutbox@=\box54
|
||||||
|
LaTeX Info: Redefining \big on input line 721.
|
||||||
|
LaTeX Info: Redefining \Big on input line 722.
|
||||||
|
LaTeX Info: Redefining \bigg on input line 723.
|
||||||
|
LaTeX Info: Redefining \Bigg on input line 724.
|
||||||
|
\big@size=\dimen155
|
||||||
|
LaTeX Font Info: Redeclaring font encoding OML on input line 742.
|
||||||
|
LaTeX Font Info: Redeclaring font encoding OMS on input line 743.
|
||||||
|
\macc@depth=\count291
|
||||||
|
LaTeX Info: Redefining \bmod on input line 904.
|
||||||
|
LaTeX Info: Redefining \pmod on input line 909.
|
||||||
|
LaTeX Info: Redefining \smash on input line 939.
|
||||||
|
LaTeX Info: Redefining \relbar on input line 969.
|
||||||
|
LaTeX Info: Redefining \Relbar on input line 970.
|
||||||
|
\c@MaxMatrixCols=\count292
|
||||||
|
\dotsspace@=\muskip17
|
||||||
|
\c@parentequation=\count293
|
||||||
|
\dspbrk@lvl=\count294
|
||||||
|
\tag@help=\toks21
|
||||||
|
\row@=\count295
|
||||||
|
\column@=\count296
|
||||||
|
\maxfields@=\count297
|
||||||
|
\andhelp@=\toks22
|
||||||
|
\eqnshift@=\dimen156
|
||||||
|
\alignsep@=\dimen157
|
||||||
|
\tagshift@=\dimen158
|
||||||
|
\tagwidth@=\dimen159
|
||||||
|
\totwidth@=\dimen160
|
||||||
|
\lineht@=\dimen161
|
||||||
|
\@envbody=\toks23
|
||||||
|
\multlinegap=\skip54
|
||||||
|
\multlinetaggap=\skip55
|
||||||
|
\mathdisplay@stack=\toks24
|
||||||
|
LaTeX Info: Redefining \[ on input line 2950.
|
||||||
|
LaTeX Info: Redefining \] on input line 2951.
|
||||||
|
) (/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amssymb.sty
|
||||||
|
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/amsfonts.sty
|
||||||
|
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||||
|
\symAMSa=\mathgroup4
|
||||||
|
\symAMSb=\mathgroup5
|
||||||
|
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||||
|
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||||
|
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||||
|
))
|
||||||
|
\c@theaufgabe=\count298
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/l3backend/l3backend-pdftex.def
|
||||||
|
File: l3backend-pdftex.def 2025-10-09 L3 backend support: PDF output (pdfTeX)
|
||||||
|
\l__color_backend_stack_int=\count299
|
||||||
|
) (./Assignment4_211.aux
|
||||||
|
Package babel Info: 'austrian' activates 'german' shorthands.
|
||||||
|
(babel) Reported on input line 6.
|
||||||
|
)
|
||||||
|
\openout1 = `Assignment4_211.aux'.
|
||||||
|
|
||||||
|
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 97.
|
||||||
|
LaTeX Font Info: ... okay on input line 97.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/context/base/mkii/supp-pdf.mkii
|
||||||
|
[Loading MPS to PDF converter (version 2006.09.02).]
|
||||||
|
\scratchcounter=\count300
|
||||||
|
\scratchdimen=\dimen162
|
||||||
|
\scratchbox=\box55
|
||||||
|
\nofMPsegments=\count301
|
||||||
|
\nofMParguments=\count302
|
||||||
|
\everyMPshowfont=\toks25
|
||||||
|
\MPscratchCnt=\count303
|
||||||
|
\MPscratchDim=\dimen163
|
||||||
|
\MPnumerator=\count304
|
||||||
|
\makeMPintoPDFobject=\count305
|
||||||
|
\everyMPtoPDFconversion=\toks26
|
||||||
|
)
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 121--123
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
LaTeX Font Info: Font shape `OT1/cmss/m/it' in size <12> not available
|
||||||
|
(Font) Font shape `OT1/cmss/m/sl' tried instead on input line 124.
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 124--125
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
<./fig/fig1.1.png, id=1, 923.45pt x 701.62125pt>
|
||||||
|
File: ./fig/fig1.1.png Graphic file (type png)
|
||||||
|
<use ./fig/fig1.1.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig1.1.png used on input line 127.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 311.2944pt.
|
||||||
|
<./fig/fig1.2.png, id=2, 940.51375pt x 568.1225pt>
|
||||||
|
File: ./fig/fig1.2.png Graphic file (type png)
|
||||||
|
<use ./fig/fig1.2.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig1.2.png used on input line 128.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 247.49538pt.
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 129--130
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
[1
|
||||||
|
|
||||||
|
{/nix/store/g8bx996bhdrf7gkgbgwh9s5xlpl0qyvv-texlive-2025-r78234-final-env/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map} <./fig/fig1.1.png> <./fig/fig1.2.png>]
|
||||||
|
LaTeX Font Info: Trying to load font information for U+msa on input line 130.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsa.fd
|
||||||
|
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
||||||
|
)
|
||||||
|
LaTeX Font Info: Trying to load font information for U+msb on input line 130.
|
||||||
|
(/nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/tex/latex/amsfonts/umsb.fd
|
||||||
|
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
||||||
|
)
|
||||||
|
<./fig/fig1.3.png, id=12, 1620.0525pt x 1124.2pt>
|
||||||
|
File: ./fig/fig1.3.png Graphic file (type png)
|
||||||
|
<use ./fig/fig1.3.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig1.3.png used on input line 153.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 284.30855pt.
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 154--155
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
[2 <./fig/fig1.3.png>]
|
||||||
|
<./fig/fig1.4.png, id=19, 835.12pt x 772.8875pt>
|
||||||
|
File: ./fig/fig1.4.png Graphic file (type png)
|
||||||
|
<use ./fig/fig1.4.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig1.4.png used on input line 194.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 379.18991pt.
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 198--199
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
[3 <./fig/fig1.4.png>]
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 211--212
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 212--213
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
<./fig/fig3.1.png, id=25, 1236.62pt x 467.7475pt>
|
||||||
|
File: ./fig/fig3.1.png Graphic file (type png)
|
||||||
|
<use ./fig/fig3.1.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig3.1.png used on input line 221.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 154.97807pt.
|
||||||
|
|
||||||
|
Underfull \hbox (badness 10000) in paragraph at lines 224--225
|
||||||
|
|
||||||
|
[]
|
||||||
|
|
||||||
|
<./fig/fig4.1.png, id=26, 839.135pt x 860.21375pt>
|
||||||
|
File: ./fig/fig4.1.png Graphic file (type png)
|
||||||
|
<use ./fig/fig4.1.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig4.1.png used on input line 228.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 420.01208pt.
|
||||||
|
[4 <./fig/fig3.1.png>]
|
||||||
|
<./fig/fig4.2.png, id=31, 836.12375pt x 851.18pt>
|
||||||
|
File: ./fig/fig4.2.png Graphic file (type png)
|
||||||
|
<use ./fig/fig4.2.png>
|
||||||
|
Package pdftex.def Info: ./fig/fig4.2.png used on input line 233.
|
||||||
|
(pdftex.def) Requested size: 409.72124pt x 417.10782pt.
|
||||||
|
[5 <./fig/fig4.1.png>] [6 <./fig/fig4.2.png>] (./Assignment4_211.aux)
|
||||||
|
***********
|
||||||
|
LaTeX2e <2025-11-01>
|
||||||
|
L3 programming layer <2026-01-19>
|
||||||
|
***********
|
||||||
|
)
|
||||||
|
Here is how much of TeX's memory you used:
|
||||||
|
4667 strings out of 467535
|
||||||
|
82020 string characters out of 5388798
|
||||||
|
491699 words of memory out of 5000000
|
||||||
|
33503 multiletter control sequences out of 15000+600000
|
||||||
|
634545 words of font info for 65 fonts, out of 8000000 for 9000
|
||||||
|
1141 hyphenation exceptions out of 8191
|
||||||
|
57i,10n,65p,280b,256s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
||||||
|
</nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmex10.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi12.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi6.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmmi8.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr12.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmr8.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssbx10.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmssi12.pfb></nix/store/56vq9r21wl8m731rsri7nh3l4ipih7jj-texlive-2025-r78234-final-env-texmfdist/fonts/type1/public/amsfonts/cm/cmsy10.pfb>
|
||||||
|
Output written on Assignment4_211.pdf (6 pages, 713525 bytes).
|
||||||
|
PDF statistics:
|
||||||
|
80 PDF objects out of 1000 (max. 8388607)
|
||||||
|
44 compressed objects within 1 object stream
|
||||||
|
0 named destinations out of 1000 (max. 500000)
|
||||||
|
36 words of extra memory for PDF output out of 10000 (max. 10000000)
|
||||||
|
|
||||||
BIN
Assignment4_211.pdf
Normal file
BIN
Assignment4_211.pdf
Normal file
Binary file not shown.
BIN
Assignment4_211.synctex.gz
Normal file
BIN
Assignment4_211.synctex.gz
Normal file
Binary file not shown.
240
Assignment4_211.tex
Normal file
240
Assignment4_211.tex
Normal file
@@ -0,0 +1,240 @@
|
|||||||
|
\documentclass[12pt,a4paper,austrian]{article}
|
||||||
|
\usepackage{graphicx}
|
||||||
|
\usepackage[austrian, english]{babel}
|
||||||
|
\usepackage[utf8]{inputenc}
|
||||||
|
%\usepackage{listings}
|
||||||
|
\usepackage{multirow}
|
||||||
|
\usepackage{epstopdf}
|
||||||
|
\usepackage{amsmath}
|
||||||
|
\usepackage{amssymb} % fuer Mengen \N, Q, C, R
|
||||||
|
\graphicspath{{./fig/}}
|
||||||
|
|
||||||
|
|
||||||
|
%% Satzspiegel
|
||||||
|
\setlength{\hoffset}{-1in} \setlength{\textwidth}{18cm}
|
||||||
|
\setlength{\oddsidemargin}{1.5cm}
|
||||||
|
\setlength{\evensidemargin}{1.5cm}
|
||||||
|
\setlength{\marginparsep}{0.7em}
|
||||||
|
\setlength{\marginparwidth}{0.5cm}
|
||||||
|
|
||||||
|
\setlength{\voffset}{-1.9in}
|
||||||
|
\setlength{\headheight}{12pt}
|
||||||
|
\setlength{\topmargin}{2.6cm}
|
||||||
|
\addtolength{\topmargin}{-\headheight}
|
||||||
|
\setlength{\headsep}{3.5cm}
|
||||||
|
\addtolength{\headsep}{-\topmargin}
|
||||||
|
\addtolength{\headsep}{-\headheight}
|
||||||
|
\setlength{\textheight}{27cm}
|
||||||
|
|
||||||
|
%% How should floats be treated?
|
||||||
|
\setlength{\floatsep}{12 pt plus 0 pt minus 8 pt}
|
||||||
|
\setlength{\textfloatsep}{12 pt plus 0pt minus 8 pt}
|
||||||
|
\setlength{\intextsep}{12 pt plus 0pt minus 8 pt}
|
||||||
|
|
||||||
|
\tolerance2000
|
||||||
|
\emergencystretch20pt
|
||||||
|
|
||||||
|
%% Text appearence
|
||||||
|
% English text
|
||||||
|
\newcommand{\eg}[1]%
|
||||||
|
{\selectlanguage{english}\textit{#1}\selectlanguage{austrian}}
|
||||||
|
|
||||||
|
\newcommand{\filename}[1]
|
||||||
|
{\begin{small}\texttt{#1}\end{small}}
|
||||||
|
|
||||||
|
\newcommand\IFT{\unitlength1mm\begin{picture}(10,2) \put (1,1)
|
||||||
|
{\circle{1.7}} \put(2,1){\line(1,0){5}} \put(8,1)
|
||||||
|
{\circle*{1.7}}\end{picture}}
|
||||||
|
\newcommand\FT{\unitlength1mm\begin{picture}(10,2) \put (1,1)
|
||||||
|
{\circle*{1.7}} \put(2,1){\line(1,0){5}} \put(8,1)
|
||||||
|
{\circle{1.7}}\end{picture}}
|
||||||
|
|
||||||
|
% A box for multiple choice problems
|
||||||
|
\newcommand{\choicebox}{\fbox{\rule{0pt}{0.5ex}\rule{0.5ex}{0pt}}}
|
||||||
|
|
||||||
|
\newenvironment{wahrfalsch}%
|
||||||
|
{\bigskip\par\noindent\makebox[1cm][c]{richtig}\hspace{3mm}\makebox[1cm][c]{falsch}
|
||||||
|
\begin{list}%
|
||||||
|
{\makebox[1cm][c]{\choicebox}\hspace{3mm}\makebox[1cm][c]{\choicebox}}%
|
||||||
|
{\setlength{\labelwidth}{2.31 cm}\setlength{\labelsep}{3mm}
|
||||||
|
\setlength{\leftmargin}{2.61 cm}\setlength{\listparindent}{0pt}
|
||||||
|
\setlength{\itemindent}{0pt}}%
|
||||||
|
}
|
||||||
|
{\end{list}}
|
||||||
|
|
||||||
|
\newcounter{theaufgabe}\setcounter{theaufgabe}{1}
|
||||||
|
\newenvironment{aufgabe}[1]%
|
||||||
|
{\bigskip\par\noindent\begin{nopagebreak}
|
||||||
|
\textsf{\textbf{\arabic{theaufgabe}.\thinspace Exercise}}\quad
|
||||||
|
\textsf{\textit{#1}}\\*[1ex]%
|
||||||
|
\stepcounter{theaufgabe}\hspace{2ex}\end{nopagebreak}}
|
||||||
|
{\par\pagebreak[2]}
|
||||||
|
|
||||||
|
% Innerhalb der Aufgaben erfolgt die weitere Unterteilung mittels einer
|
||||||
|
% enumerate Umgebung, die allerdings a), b),... zaehlen soll.
|
||||||
|
\renewcommand{\labelenumi}{\alph{enumi})}
|
||||||
|
\renewcommand{\labelenumii}{\arabic{enumii})}
|
||||||
|
|
||||||
|
% A box to tick for everything which has to done
|
||||||
|
\newcommand{\abgabe}{\marginpar{$\Box$}}
|
||||||
|
% Margin paragraphs on the left side
|
||||||
|
\reversemarginpar
|
||||||
|
|
||||||
|
% Language for listings
|
||||||
|
%\lstset{language=Vhdl,
|
||||||
|
% basicstyle=\small\tt,
|
||||||
|
% keywordstyle=\tt\bf,
|
||||||
|
% commentstyle=\sl}
|
||||||
|
|
||||||
|
% No indention
|
||||||
|
\setlength{\parindent}{0.0cm}
|
||||||
|
% Don't number sections
|
||||||
|
\setcounter{secnumdepth}{0}
|
||||||
|
|
||||||
|
|
||||||
|
%% Beginning of the text
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\selectlanguage{austrian}
|
||||||
|
\pagestyle{plain}
|
||||||
|
|
||||||
|
|
||||||
|
%=== This is the header section ============================================================
|
||||||
|
\thispagestyle{empty}
|
||||||
|
\noindent
|
||||||
|
\begin{minipage}[b][4cm]{1.0\textwidth}
|
||||||
|
\begin{center}
|
||||||
|
\begin{bf}
|
||||||
|
\begin{large} Digitale Signalverarbeitung SS 2025/26 -- 4.~Aufgabe\end{large} \\
|
||||||
|
\vspace{0.3cm}
|
||||||
|
\begin{Large} Reconstruction, DFT, FFT \end{Large} \\
|
||||||
|
\vspace{0.3cm}
|
||||||
|
\end{bf}
|
||||||
|
\begin{large}
|
||||||
|
Gruppennummer 211 \\
|
||||||
|
Manuel Illmayer, k12308149 \\
|
||||||
|
Quirin Ecker, k12310122 \\
|
||||||
|
\end{large}
|
||||||
|
\end{center}
|
||||||
|
\end{minipage}
|
||||||
|
|
||||||
|
\noindent \rule[0.8em]{\textwidth}{0.12mm}\\[-0.5em]
|
||||||
|
%=======================================================================================
|
||||||
|
|
||||||
|
\begin{aufgabe}{Reconstruction}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item : \\
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig1.1.png} \\
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig1.2.png}
|
||||||
|
\item : \\
|
||||||
|
\begin{gather*}
|
||||||
|
x(t) = 1 + 0.5 \cos(2\pi f_1 t) + 2 \sin(2\pi f_2 t) + \sin(2\pi f_3 t) \\
|
||||||
|
\end{gather*}
|
||||||
|
|
||||||
|
Calculation of $x_1[n]$:
|
||||||
|
|
||||||
|
\begin{gather*}
|
||||||
|
x(t) = 1 + 0.5 \cos(2\pi f_1 t) + 2 \sin(2\pi f_2 t) + \sin(2\pi f_3 t) \\
|
||||||
|
= 1 + 0.5 \cos(2\pi 2000 t) + 2 \sin(2\pi 4000 t) + \sin(2\pi 6000 t) \\
|
||||||
|
x_1[n] = 1 + 0.5 \cos(2\pi \frac{2000}{9000} n) + 2 \sin(2\pi \frac{4000}{9000} n) + \sin(2\pi \frac{6000}{9000} n) \\
|
||||||
|
= 1 + 0.5 \cos(\frac{4 \pi}{9} n) + 2 \sin( \frac{8 \pi}{9} n) + \sin( \frac{4 \pi}{3} n) \\
|
||||||
|
\\
|
||||||
|
\sin(\frac{4 \pi}{3}) = -\sin(\frac{2 \pi}{3})
|
||||||
|
\\
|
||||||
|
\implies x_1[n]= 1 + 0.5 \cos(\frac{4 \pi}{9} n) + 2 \sin( \frac{8 \pi}{9} n) - \sin( \frac{2 \pi}{3} n)
|
||||||
|
\end{gather*}
|
||||||
|
|
||||||
|
Calculation of $x_2[n]$:
|
||||||
|
|
||||||
|
\begin{gather*}
|
||||||
|
x_1[n] = 1 + 0.5 \cos(2\pi \frac{2000}{14000} n) + 2 \sin(2\pi \frac{4000}{14000} n) + \sin(2\pi \frac{6000}{14000} n) \\
|
||||||
|
= 1 + 0.5 \cos(\frac{2 \pi}{7} n) + 2 \sin( \frac{4 \pi}{7} n) + \sin( \frac{6 \pi}{7} n) \\
|
||||||
|
\end{gather*}
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig1.3.png}
|
||||||
|
\item: \\
|
||||||
|
|
||||||
|
\[
|
||||||
|
f=\frac{\Omega f_s}{2\pi}
|
||||||
|
\]
|
||||||
|
|
||||||
|
Calculations for $x_1(t)$:
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_1=\frac{\Omega_1 f_s}{2\pi}
|
||||||
|
=\frac{\left(\frac{4\pi}{9}\right)9000}{2\pi}
|
||||||
|
=2000
|
||||||
|
\]
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_2 = ... = 4000
|
||||||
|
\]
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_3=\frac{\Omega_3 f_s}{2\pi}
|
||||||
|
=\frac{\left(-\frac{2\pi}{3}\right)9000}{2\pi}
|
||||||
|
=-3000
|
||||||
|
\]
|
||||||
|
|
||||||
|
Calculations for $x_2(t)$:
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_1 = ... = 2000
|
||||||
|
\]
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_2 = ... = 4000
|
||||||
|
\]
|
||||||
|
|
||||||
|
\[
|
||||||
|
f_3 = ... = 6000
|
||||||
|
\]
|
||||||
|
|
||||||
|
Where '...' is just the formular at the top injected with the $\Omega$ values of b)
|
||||||
|
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig1.4.png}
|
||||||
|
\end{enumerate}
|
||||||
|
\end{aufgabe}
|
||||||
|
|
||||||
|
\begin{aufgabe}{DFT Theory}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item
|
||||||
|
\begin{gather*}
|
||||||
|
f_s = \frac{1}{T_s} = \frac{1}{0.001} = 1000 \text{Hz} \\
|
||||||
|
\Delta f = \frac{f_s}{N} = \frac{1000}{100} = 10 \text{Hz} \\
|
||||||
|
\end{gather*}
|
||||||
|
\item
|
||||||
|
\begin{gather*}
|
||||||
|
\text{In terms of samples}: 100 \\
|
||||||
|
\text{In terms of frequency}: N \cdot \Delta f_s = 1000 \text{Hz} \\
|
||||||
|
\text{In terms of angular frequency}: \omega = 2 \pi \frac{f}{f_s} = 2 \pi \frac{1000}{1000} = 2 \pi
|
||||||
|
\end{gather*}
|
||||||
|
\item Computers can calculate it more efficently when it is working with powers of two \\
|
||||||
|
\item $\Delta f = \frac{f_s}{N} = \frac{1000}{128} = 7.8125 \text{Hz}$ \\
|
||||||
|
\item Even though we have not gained new information, we have a finer resolution of the frequency axis. This can make it easier to get closer to the actual value.
|
||||||
|
\end{enumerate}
|
||||||
|
\end{aufgabe}
|
||||||
|
|
||||||
|
\begin{aufgabe}{FFT in Image Processing}
|
||||||
|
Approach: We want to remove the low frequencies (high pass filter) to
|
||||||
|
keep the areas of the image where the lightness changes relative to
|
||||||
|
nearby pixels \\
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig3.1.png}
|
||||||
|
\end{aufgabe}
|
||||||
|
|
||||||
|
\begin{aufgabe}{Window Effects of the DFT}
|
||||||
|
\begin{enumerate}
|
||||||
|
\item ( see b) )
|
||||||
|
\item (see assignment4\_4.m) \\
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig4.1.png}
|
||||||
|
\item
|
||||||
|
Rectangular window: Clear peaks but also many neighbors have fairly high values
|
||||||
|
Hamming window: Still visible peaks, that may be a bit wider, but now clearly separated from neighbors and more visually readable.
|
||||||
|
\item We can choose freqencies that align with our 128 steps, for example f1 = 10/N and f2 = 15/N. With this, the signal fits exactly within our window, each cosine has a integer number of cycles it completes \\
|
||||||
|
\includegraphics[width=0.8\textwidth]{./fig/fig4.2.png}
|
||||||
|
\end{enumerate}
|
||||||
|
|
||||||
|
|
||||||
|
\end{aufgabe}
|
||||||
|
|
||||||
|
|
||||||
|
\end{document}
|
||||||
BIN
Assignment4_211.zip
Normal file
BIN
Assignment4_211.zip
Normal file
Binary file not shown.
33
Assignment4_211/assignment4.4.m
Normal file
33
Assignment4_211/assignment4.4.m
Normal file
@@ -0,0 +1,33 @@
|
|||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
N = 128;
|
||||||
|
n = 0:N-1;
|
||||||
|
w1 = 2*pi*0.1;
|
||||||
|
w2 = 2*pi*0.15;
|
||||||
|
x = cos(w1*n) + cos(w2*n);
|
||||||
|
|
||||||
|
% a)
|
||||||
|
|
||||||
|
X = fft(x);
|
||||||
|
magX = abs(X);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
stem(n, magX, 'filled');
|
||||||
|
xlabel('n');
|
||||||
|
ylabel('|X[n]|');
|
||||||
|
title('Magnitude Spectrum of x[n]');
|
||||||
|
grid on;
|
||||||
|
|
||||||
|
% b)
|
||||||
|
|
||||||
|
y = hamming(N)' .* x;
|
||||||
|
|
||||||
|
Y = fft(y);
|
||||||
|
magY = abs(Y);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
stem(n, magY, 'filled');
|
||||||
|
xlabel('n');
|
||||||
|
ylabel('|Y[n]|');
|
||||||
|
title('Magnitude Spectrum of y[n]');
|
||||||
|
grid on;
|
||||||
33
Assignment4_211/assignment4_1.m
Normal file
33
Assignment4_211/assignment4_1.m
Normal file
@@ -0,0 +1,33 @@
|
|||||||
|
clc;
|
||||||
|
clear;
|
||||||
|
close all;
|
||||||
|
|
||||||
|
%% Parameters
|
||||||
|
f1 = 2000;
|
||||||
|
f2 = 4000;
|
||||||
|
f3 = 6000;
|
||||||
|
|
||||||
|
f3_rec = -3000
|
||||||
|
|
||||||
|
%% Time vectors
|
||||||
|
t=0:1e-6:1e-3;
|
||||||
|
|
||||||
|
%% Signals
|
||||||
|
x = 1+0.5*cos(2*pi*f1*t)+2*sin(2*pi*f2*t)+sin(2*pi*f3*t);
|
||||||
|
x1 = 1+0.5*cos(2*pi*f1*t)+2*sin(2*pi*f2*t)+sin(2*pi*f3_rec*t);
|
||||||
|
x2 = 1+0.5*cos(2*pi*f1*t)+2*sin(2*pi*f2*t)+sin(2*pi*f3*t);
|
||||||
|
|
||||||
|
%% Plot
|
||||||
|
figure
|
||||||
|
hold on
|
||||||
|
|
||||||
|
plot(t, x, 'b', 'LineWidth', 1.5)
|
||||||
|
plot(t, x1, 'r', 'LineWidth', 1.5)
|
||||||
|
plot(t, x2, '--g', 'LineWidth', 1.5)
|
||||||
|
|
||||||
|
grid on
|
||||||
|
|
||||||
|
xlabel('Time (ms)')
|
||||||
|
ylabel('x(t)')
|
||||||
|
|
||||||
|
legend('x(t)', 'x1(t)', 'x2(t)');
|
||||||
51
Assignment4_211/assignment4_3.m
Normal file
51
Assignment4_211/assignment4_3.m
Normal file
@@ -0,0 +1,51 @@
|
|||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
img = imread('pavian.png'); % Choose any picture you like here
|
||||||
|
img = rgb2gray(img);
|
||||||
|
|
||||||
|
%% Display image
|
||||||
|
figure; subplot(131);
|
||||||
|
imshow(img);
|
||||||
|
title('Ausgangsbild');
|
||||||
|
|
||||||
|
%% FFT
|
||||||
|
fft2d = fft2(img);
|
||||||
|
|
||||||
|
% Display the FFT image.
|
||||||
|
subplot(132);
|
||||||
|
imshow(log(fftshift(abs(fft2d))), []);
|
||||||
|
title('2D-FFT');
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%%
|
||||||
|
|
||||||
|
% Approach: We want to remove the low frequencies (high pass filter) to
|
||||||
|
% keep the areas of the image where the lightness changes relative to
|
||||||
|
% nearby pixels
|
||||||
|
|
||||||
|
% Shift FFT so low frequencies are in the center
|
||||||
|
F = fftshift(fft2d);
|
||||||
|
|
||||||
|
% Get image size
|
||||||
|
[M, N] = size(F);
|
||||||
|
|
||||||
|
% Radius of how much to remove
|
||||||
|
r = 25;
|
||||||
|
|
||||||
|
% We cut out the center of the fft low frequencies
|
||||||
|
H = ones(M, N);
|
||||||
|
H(M/2-r:M/2+r, N/2-r:N/2+r) = 0;
|
||||||
|
|
||||||
|
% Apply filter
|
||||||
|
F_filtered = F .* H;
|
||||||
|
|
||||||
|
% Shift back
|
||||||
|
fft2d = ifftshift(F_filtered);
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%% IFFT to obtain filtered image
|
||||||
|
img_filtered = ifft2(fft2d);
|
||||||
|
subplot(133);
|
||||||
|
imshow(real(img_filtered), []);
|
||||||
|
title('Gefiltertes Ausgangssignal');
|
||||||
BIN
fig/fig1.1.png
Normal file
BIN
fig/fig1.1.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 29 KiB |
BIN
fig/fig1.2.png
Normal file
BIN
fig/fig1.2.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 23 KiB |
BIN
fig/fig1.3.png
Normal file
BIN
fig/fig1.3.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 102 KiB |
BIN
fig/fig1.4.png
Normal file
BIN
fig/fig1.4.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 50 KiB |
BIN
fig/fig3.1.png
Normal file
BIN
fig/fig3.1.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 354 KiB |
BIN
fig/fig4.1.png
Normal file
BIN
fig/fig4.1.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 31 KiB |
BIN
fig/fig4.2.png
Normal file
BIN
fig/fig4.2.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 28 KiB |
26
flake.lock
generated
Normal file
26
flake.lock
generated
Normal file
@@ -0,0 +1,26 @@
|
|||||||
|
{
|
||||||
|
"nodes": {
|
||||||
|
"nixpkgs": {
|
||||||
|
"locked": {
|
||||||
|
"lastModified": 1779017031,
|
||||||
|
"narHash": "sha256-bSFtTjXkh80yk4RfdQXQ9mCtHTG7mwJrVXpolJeXqsQ=",
|
||||||
|
"owner": "NixOS",
|
||||||
|
"repo": "nixpkgs",
|
||||||
|
"rev": "71b4e08640c2222a2aad7777b6936edb2ea1ccb7",
|
||||||
|
"type": "github"
|
||||||
|
},
|
||||||
|
"original": {
|
||||||
|
"owner": "NixOS",
|
||||||
|
"repo": "nixpkgs",
|
||||||
|
"type": "github"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"root": {
|
||||||
|
"inputs": {
|
||||||
|
"nixpkgs": "nixpkgs"
|
||||||
|
}
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"root": "root",
|
||||||
|
"version": 7
|
||||||
|
}
|
||||||
23
flake.nix
Normal file
23
flake.nix
Normal file
@@ -0,0 +1,23 @@
|
|||||||
|
{
|
||||||
|
description = "LaTeX paper build environment";
|
||||||
|
|
||||||
|
inputs = {
|
||||||
|
nixpkgs.url = "github:NixOS/nixpkgs";
|
||||||
|
};
|
||||||
|
|
||||||
|
outputs =
|
||||||
|
{ self, nixpkgs }:
|
||||||
|
let
|
||||||
|
system = "x86_64-linux";
|
||||||
|
pkgs = import nixpkgs { inherit system; };
|
||||||
|
in
|
||||||
|
{
|
||||||
|
devShells.${system}.default = pkgs.mkShell {
|
||||||
|
name = "latex";
|
||||||
|
buildInputs = with pkgs; [
|
||||||
|
texliveFull
|
||||||
|
octave
|
||||||
|
];
|
||||||
|
};
|
||||||
|
};
|
||||||
|
}
|
||||||
Reference in New Issue
Block a user