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f1 = 1; N = 800; % Number of Samples Fs = 50; % Sampling Frequency in Hz alpha = 0.05; t = ((-N/2):(N/2)-1)/Fs; y = 1sin(2pif1t); % sine wave noise = alpha.*(randn(size(y))); y = y + noise; rectWindow = rectwin(length(t))'; % Rectangular Window hammingWindow = hamming(length(t))'; % Hamming Window % Rectangular Window ACF & PSD figure('Name','Rectangular Window ACF & PSD'); plot(t,y),title('Sine Wave'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; plot(t,rectWindow),title('Rectangular Window'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; rectangularSignalWithNoise = y.rectWindow; plot(t,rectangularSignalWithNoise),title('Windowed Signal'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; [correlationSignal1, rectShifted] = xcorr(rectangularSignalWithNoise, 'biased'); timeDifferenceofR = rectShifted1/Fs; plot(timeDifferenceofR,correlationSignal1),title('ACF using Rectangular Window'), xlabel('Time difference \tau (in sec)'), ylabel('Amplitude') figure; % Power Spectral Density using Wiener Khintchine Theorem with Rectangular window Rxxdft1 = abs(fftshift(fft(correlationSignal1)))/N; freq1 = -Fs/2:Fs/length(correlationSignal1):Fs/2- (Fs/length(correlationSignal1)); plot(freq1,Rxxdft1),title({'Power Spectral Density using Wiener Khintchine Theorem ', 'with Rectangular window'}), xlabel('Frequency f (in Hz)'),ylabel('Spectral Power') figure; % Power Spectral Density using ftsquared with Rectangular window ftsquareMethod = abs(fftshift(fft(rectangularSignalWithNoise)))/N; ftsquareMethod = (ftsquareMethod.*ftsquareMethod); freq2 = -Fs/2:Fs/length(sig1):Fs/2- (Fs/length(rectangularSignalWithNoise)); plot(freq2, ftsquareMethod) title('fourier sqaure method'), title({'Power Spectral Density using FTS squared theorem ', 'with Rectangular window'}), xlabel('Frequency f (in Hz)'),ylabel('Spectral Power') figure; % Hamming Window ACF & PSD plot(t,y),title('Signal with Noise'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; plot(t,hammingWindow),title('Hamming Window'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; hammingSignalWithNoise = y.hammingWindow; plot(t,hammingSignalWithNoise),title('Windowed Signal'),ylim([-1.5 1.5]), xlabel('Time (in sec)'), ylabel('Amplitude') figure; [correlationSignal2, hamShifted] = xcorr(hammingSignalWithNoise, 'biased'); timeDifferenceofH = hamShifted1/Fs; plot(hamShifted,correlationSignal2),title('ACF using Hamming Window'), xlabel('Time difference \tau (in sec)'), ylabel('Amplitude') figure; Rxxdft2 = abs(fftshift(fft(correlationSignal2)))/N; freq2 = -Fs/2:Fs/length(r2):Fs/2- (Fs/length(correlationSignal2)); plot(freq2,Rxxdft2),title({'Power Spectral Density using Wiener Khintchine Theorem ', 'with Hamming window'}),xlim([-50 50]), xlabel('Frequency f (in Hz)'),ylabel('Spectral Power') figure; % Power Spectral Density using ftsquared with Hamming window ftsquareMethod = abs(fftshift(fft(hammingSignalWithNoise)))/N; ftsquareMethod = (ftsquareMethod.*ftsquareMethod); freq2 = -Fs/2:Fs/length(sig2):Fs/2- (Fs/length(hammingSignalWithNoise)); plot(freq2, ftsquareMethod) title('fourier sqaure method'), title({'Power Spectral Density using FTS squared theorem ', 'with Hamming window'}), xlabel('Frequency f (in Hz)'),ylabel('Spectral Power') figure;