finished exercise except for some parts of number 1

Assignment2_211/assignment2_1.m

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+clear
+close all
+clc
+
+% x1[n], -5 <= n <= 10
+n1 = -5:10;
+x1 = -4*(n1 == -3) + 4*(n1 == 0) - (n1 == 3) + 2*(n1 == 7);
+
+% x2[n], -5 <= n <= 10
+n2 = -5:10;
+x2 = exp(-0.31*n2);
+
+% x3[n], 0 <= n <= 256
+n3 = 0:256;
+x3 = 3*sin(2*pi*(3.5/64)*n3);
+
+% x4[n], 0 <= n <= 256
+n4 = 0:256;
+x4 = -cos((9/64)*n4);
+
+
+% Visualization
+figure;
+subplot(121); hold on; grid on;
+stem(n1, x1);
+stem(n2, x2);
+xlabel('n');
+ylabel('x[n]');
+legend('x_1[n]', 'x_2[n]');
+
+subplot(122); hold on; grid on;
+plot(n3, x3);
+plot(n4, x4);
+xlabel('n');
+ylabel('x[n]');
+legend('x_3[n]', 'x_4[n]');
+
+% Custom power function
+function [ P ] = custom_power( x )
+    P = (1/length(x)) * sum(abs(x).^2);
+end
+
+% Calculate and display the power
+P3 = custom_power(x3);
+% Display the calculated powers
+disp(['Power of x_3[n]: ', num2str(P3)]);
+
+% Energy function
+function [ W ] = energy( x )
+    W = sum(abs(x).^2);
+end
+
+% Calculate and display the energy of each signal
+P1 = energy(x1);
+P2 = energy(x2);
+P3 = energy(x3);
+P4 = energy(x4);
+% Display the calculated powers
+disp(['Energy of x_1[n]: ', num2str(P1)]);
+disp(['Energy of x_2[n]: ', num2str(P2)]);
+disp(['Energy of x_3[n]: ', num2str(P3)]);
+disp(['Energy of x_4[n]: ', num2str(P4)]);

Assignment2_211/assignment2_3.m

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+clear
+close all
+clc
+
+
+% Convolution function
+function [ Y ] = convolution( h, x )
+    Ny = length(x)+length(h)-1
+    Y = zeros(1, Ny);
+    for n = 1:Ny
+        for i = 1:length(h)
+            if (n-i+1 >= 1) && (n-i+1 <= length(x))
+                Y(n) = Y(n) + h(i) * x(n-i+1)
+            end
+        end
+    end
+end
+
+n = 0:49
+hn = [0.25, 0.5, 0.25]
+xn = cos(((2*pi)/20)*n)
+
+% Perform convolution of xn and hn
+Y = convolution(hn, xn);
+Y2 = conv(xn, hn)
+
+% Plot the results
+plot(Y);
+xlabel('Sample Index');
+ylabel('Amplitude');
+title('Convolution Result');
+grid on;
+
+% Plot Y2 on same graph
+hold on;
+plot(Y2, '--');
+legend('Custom Convolution', 'MATLAB conv Function');
+hold off;
+

Assignment2_211/assignment2_4.m

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+function X = dtft ( x , n , w )
+    % DTFT Computes Discrete-time Fourier transform
+    % @param x : finite duration sequence (vector) over n
+    % @param n : sample indices vector
+    % @param w : frequency vector
+    % @return X : DTFT of x[n] at frequencies w
+    % this function does not use for loops
+    X = sum(x(:) .* exp(-1j * n(:) * w), 1);
+end
+
+n = -10:10;
+x = (0.8) .^ abs(n) .* ((n >= -10) & (n < 11));
+w = linspace(-pi, pi, 1000);
+
+X = dtft(x, n, w);
+
+magnitude = abs(X);
+phase = angle(X);
+figure;
+subplot(2, 1, 1);
+plot(w, magnitude);
+title('Magnitude Response');
+xlabel('Frequency (rad/sample)');
+ylabel('|X(w)|');
+subplot(2, 1, 2);
+plot(w, phase);
+title('Phase Response');
+xlabel('Frequency (rad/sample)');
+ylabel('Phase(rad)');

Assignment2_211/assignment2_5.m

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+% Read and play original audio
+[audio, fs] = audioread('./audio.wav');
+%sound(audio, fs);
+
+% Read and play room impulse response (RIR)
+[rir, fs_rir] = audioread('./rir.wav');
+%sound(rir, fs_rir);
+
+% Apply convolution (reverb effect)
+audio_reverb = conv(audio, rir);
+
+%sound(audio_reverb, fs);
+
+% Plot the waveforms
+figure;
+
+% Original audio
+subplot(2,1,1);
+plot(audio);
+title('Original Audio');
+xlabel('Sample Number');
+ylabel('Amplitude');
+
+% Reverberated audio
+subplot(2,1,2);
+plot(audio_reverb);
+title('Audio with Reverb');
+xlabel('Sample Number');
+ylabel('Amplitude');
+
+% Calculate signal energy
+function [ W ] = energy( x )
+    W = sum(abs(x).^2);
+end
+
+energy_rir = energy(rir)
+energy_original = energy(audio)
+energy_reverb = energy(audio_reverb)
+
+% Display energy values
+fprintf('Original Audio Energy: %.4f\n', energy_original);
+fprintf('Reverberated Audio Energy: %.4f\n', energy_reverb);