N=256; %% sampling number

n=linspace(0,1,N);

fs=1/(n(2)-n(1));

x=5*(sin((2*pi*10*n)+deg2rad(30))); %% creat signal

figure;

N=length(x);

f=[-fs/2:fs/N:fs/2-fs/N];

subplot(211)

plot(f,fftshift(abs(fft(x))),'b');

title('|G(f)|');grid;

xlabel('frequency');

ylabel('|G(f)|');

%Zero padding

xx=[zeros(1,128) x zeros(1,128)];

N=length(xx);

f=[-fs/2:fs/N:fs/2-fs/N];

subplot(212)

plot(f,fftshift(abs(fft(xx))),'r');

title('|Gz(f)|');grid;

xlabel('frequency');

ylabel('|Gz(f)|');

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Question : Use upper code. Let's say IFFT the above fz(f) function is gz(nTs). Plot the function spectrum (N = 512)

1. Plot the spectrum of the function g1[m] (m = 1,2,3 ... 128) generated by changing the sampling interval Ts of gz(t) to 4Ts. (Observe aliasing)

2. Plot the spectrum of the function g2[m] (m = 1,2,3 ... 256) generated by changing the sampling interval Ts of gz(t) to 2Ts.

3. Plot the spectrum zero-padding g2[m] by 128 left and right.

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You can use reference code below.

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%% Create discrete signal % create x[n]=0.4cos(0.7n) n=1:0.01:100; %time vector figure(1); plot(n,0.4*cos(0.7*pi*n)); %signal generation xlabel('time'); ylabel('amplitude'); title('0.4cos(0.7n) graph');

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%% convolution % Find the convolution of the input signal x[n] and the LTI system h[n] a=[0 0 1 1 1 1 1 0 0]; b=[0 0 2 2 2 2 2 0 0]; %signal generation convolution=conv(a,b); %convolution m=length(convolution)-1; n=0:1:m; figure(2) plot(n,convolution); xlabel('time'); ylabel('amplitude'); title('convolution graph');

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%% FFT %Fourier transform after signal generation

Fs= 100; % sampling frequency Ts=1/Fs; %sampling time T=100; %length of time t=linspace(0,T,T/Ts); %time vector

x=0.4*cos(2*pi*30*t); %signal generation f=linspace(-Fs/2,Fs/2,length(t)); %frequency vector fft_x=fftshift(fft(x)); %FFT abs_fft_x=abs(fft_x); figure(3) plot(f,abs_fft_x); title('FFT') xlabel('frequency'); ylabel('magnitude');

Thanks in advance :)