Swap the left and right halves of a row vector. If a vector has an odd number of elements, then the middle element is considered part of the left half of the vector.

Xeven = [1 2 3 4 5 6]; fftshift(Xeven)

ans =1×64 5 6 1 2 3

Xodd = [1 2 3 4 5 6 7]; fftshift(Xodd)

ans =1×75 6 7 1 2 3 4

When analyzing the frequency components of signals, it can be helpful to shift the zero-frequency components to the center.

Create a signalS, compute its Fourier transform, and plot the power.

fs = 100;% sampling frequencyt = 0:(1/fs):(10-1/fs);% time vectorS = cos(2*pi*15*t); n = length(S); X = fft(S); f = (0:n-1)*(fs/n);%frequency rangepower = abs(X).^2/n;%powerplot(f,power)

Shift the zero-frequency components and plot the zero-centered power.

Y = fftshift(X); fshift = (-n/2:n/2-1)*(fs/n);% zero-centered frequency rangepowershift = abs(Y).^2/n;% zero-centered powerplot(fshift,powershift)

You can process multiple 1-D signals by representing them as rows in a matrix. Then use the dimension argument to compute the Fourier transform and shift the zero-frequency components for each row.

Create a matrixAwhose rows represent two 1-D signals, and compute the Fourier transform of each signal. Plot the power for each signal.

fs = 100;% sampling frequencyt = 0:(1/fs):(10-1/fs);% time vectorS1 = cos(2*pi*15*t); S2 = cos(2*pi*30*t); n = length(S1); A = [S1; S2]; X = fft(A,[],2); f = (0:n-1)*(fs/n);% frequency rangepower = abs(X).^2/n;% powerplot(f,power(1,:),f,power(2,:))

Shift the zero-frequency components, and plot the zero-centered power of each signal.

Y = fftshift(X,2); fshift = (-n/2:n/2-1)*(fs/n);% zero-centered frequency rangepowershift = abs(Y).^2/n;% zero-centered powerplot(fshift,powershift(1,:),fshift,powershift(2,:))