How to use FFTshift to produce a 0 frequency centered plot

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

[Star Strider]

What precisely is the problem?

The right plot looks to be the appropriate result after using fftshift.

What were you expecting?

.

[Yian Chen]

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.

Answer 1

[Ashutosh Singh Baghel]

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'.