finished exercise

Assignment1_211.tex

@@ -154,7 +154,7 @@ c_4 &= c_1 + c_2
 \begin{align*}
 c_5 &= c_1 \cdot c_2
 = \left(\sqrt{34}\, e^{-j\,0.54}\right)\left(\frac{\sqrt{2}}{2} e^{-j \frac{3 \pi}{4}}\right)
-\approx \frac{\sqrt{70}}{2} e^{-j\,2.8961} \\
+\approx \sqrt{17} e^{-j\,2.8961} \\
 \end{align*}
 
 \begin{align*}
@@ -276,11 +276,11 @@ y_1(t) \ne y_2(t)
 
 
 \[
-    y_1(t) &= \left(x(t - \alpha)\right)^2 \\
+    y_1(t) &= \left(x(t - \Delta)\right)^2 \\
 \]
 
 \[
-    y_2(t) &= y_1(t - \Delta) = \left(x(t - \alpha)\right)^2 \\
+    y_2(t) &= y_1(t - \Delta) = \left(x(t - \Delta)\right)^2 \\
 \]
 
 \[
@@ -290,18 +290,18 @@ y_1(t) \ne y_2(t)
 \[
 \implies \text{Time invariant}
 \]
-	\item $y(t) = w(t) sin(\Omega_0 t)$
+	\item $y(t) = x(t) sin(\Omega_0 t)$
 
 \[
-	y(t) &= x(t) \sin(n \Omega_0 t) \\
+	y(t) &= x(t) \sin(\Omega_0 t) \\
 \]
 
 \[
-	y_1(t) &= \left( \alpha \, x(t) \sin(n_1 \omega t) \right) + \left( \beta \, x(t) \sin(n_0 t) \right) \\
+	y_1(t) &= \left( \alpha \, x(t) \sin(\Omega_0 t) \right) + \left( \beta \, x(t) \sin(\Omega_0 t) \right) \\
 \]
 
 \[
-	y_t(t) &= \alpha \left( x(t) \sin(n_1 \omega t) \right) + \beta \left( x(t) \sin(n_0 t) \right) \\
+	y_t(t) &= \alpha \left( x(t) \sin(\Omega_0 t) \right) + \beta \left( x(t) \sin(\Omega_0 t) \right) \\
 \]
 
 \[
@@ -316,11 +316,11 @@ y_1(t) \ne y_2(t)
 
 
 \[
-    y_1(t) &\coloneqq x(t - \alpha) \sin(\omega_0 t - \alpha) \\
+    y_1(t) = &\coloneqq x(t - \Delta) \sin(\Omega_0 t - \Delta) \\
 \]
 
 \[
-    y_2(t) &= y_1(t - \alpha) = x(t - \alpha) \sin(\omega_0 t - \alpha) \\
+    y_2(t) &= y_1(t - \Delta) = x(t - \Delta) \sin(\Omega_0 t - \Delta) \\
 \]
 
 \[