# recreating nyquist regions using FFT

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fima v il 17 Mar 2023
Risposto: Paul il 18 Mar 2023
Hello,Using code bellowI have sampled a signal and made FFT to see the spectral picture of the time domain signal. the plot bellow shows only 1st and 2nd nyquist zone. I want to expend the spectral image and see the 3rd and 4th nyquist zones.
i have tried to double number of samples but it only expand the previos image two times. where did i go wrong recreating addional nyquist zones? Thanks.
clc
clear all
Fs=200e3;
Ts=1/Fs;
dt=0:Ts:5e-3-Ts;
f1=1e3;
f2=20e3;
f3=30e3;
y=5*sin(2*pi*f1*dt)+5*sin(2*pi*f2*dt)+10*sin(2*pi*f3*dt);
%plot(dt,y)
nfft=length(y);
nfft2=1000;
fy=fft(y,nfft2);
f_half=2*fy(1:(nfft2));
xfft=Fs.*(0:(nfft2)-1)/nfft2;
plot(xfft,abs(f_half)/(nfft));
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### Risposte (1)

Paul il 18 Mar 2023
Are the "third" and "fourth" Nyquist zone the frequencies from Fs to 3*Fs/2 and from 3*Fs/2 to 2*Fs respectively? If so, third is just a copy of the first and the fourth is just a copy of the second, because the Discrete Time Fourier Transform is periodic with period Fs. So, if a plot is really desired it's just
clc
clear all
Fs=200e3;
Ts=1/Fs;
dt=0:Ts:5e-3-Ts;
f1=1e3;
f2=20e3;
f3=30e3;
y=5*sin(2*pi*f1*dt)+5*sin(2*pi*f2*dt)+10*sin(2*pi*f3*dt);
%plot(dt,y)
nfft=length(y);
nfft2=1000;
fy=fft(y,nfft2);
Not sure why fy is being multiplied by 2? But we'll keep it ...
f_half=2*fy(1:(nfft2));
f_half = repmat(f_half,1,2);
xfft=Fs.*(0:(numel(f_half))-1)/numel(f_half)*2;
plot(xfft,abs(f_half)/(nfft));
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