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How to use FFTshift to produce a 0 frequency centered plot

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Here is my plot, but I don't know why the right plot is shifted after using FFTshift function, how can I solve this problem?
fs = 250;
t = (0:1/fs:(0.1-.5/fs)); % [0, 0.1)
g = sin(2*pi*50*t)+0.3;
plot(t, g,'-o'),
title('g(t) = sin(2 * pi * 50 * t)+0.3' );
xlabel('time/s');
ylabel('g(t) ');
grid on
n = length(g);
L = 25;
Y = fft(g);
f = fs*(0:L-1)/L;
G = fftshift(Y);
fshift = (-n/2:n/2-1)*(fs/n); % zero-centered frequency range
powershift = abs(G).^2/n; % zero-centered power
figure
plot(fshift,powershift,'-o') % zero-centered plot which have shifts
grid on
figure
plot(f, abs(Y),'-o'), % correct frequency plot
xlabel 'Frequency (Hz)';
ylabel 'Magnitude';
title('Magnitude Plot');
grid on
  2 Comments
Yian Chen
Yian Chen on 28 Sep 2021
Hi, thanks for your answer, if you observe the the right plot, you can see that the peaks are exactly not 50Hz,may be less than 50Hz, and not zero-centered. I just wanna figure out why and how to solve.

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Accepted Answer

Ashutosh Singh Baghel
Ashutosh Singh Baghel on 18 Oct 2021
Hi Yian,
I understand your curves and data values are true, yet the plot is shifted left by "-5". Please try to update the starting and final value of 'fshift' to,
fs = 250;
t = (0:1/fs:(0.1-.5/fs)); % [0, 0.1)
g = sin(2*pi*50*t)+0.3;
n = length(g);
L = 25;
Y = fft(g);
f = fs*(0:L-1)/L;
G1 = abs(Y);
G = fftshift(Y);
fshift = (-(n+1)/2+1:(n)/2)*(fs/n) % zero-centered frequency range
fshift = 1×25
-120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120
powershift = abs(G).^2/n; % zero-centered power
figure
plot(fshift(1:end),powershift(1:end),'-o');% zero-centered plot which have shifts
grid on
Please find the MATLAB documentation link for 'fftshift'.

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