fftshift

Shift zero-frequency component to center of spectrum

Syntax

Y = fftshift(X)

Y = fftshift(X,dim)

Description

Y = fftshift(X) rearranges a Fourier transform X by shifting the zero-frequency component to the center of the array.

• If X is a vector, then fftshift swaps the left and right halves of X.

• If X is a matrix, then fftshift swaps the first quadrant of X with the third, and the second quadrant with the fourth.

• If X is a multidimensional array, then fftshift swaps half-spaces of X along each dimension.

Y = fftshift(X,dim) operates along the dimension dim of X. For example, if X is a matrix whose rows represent multiple 1-D transforms, then fftshift(X,2) swaps the halves of each row of X.

Examples

Shift Vector Elements

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 = 1×6

     4     5     6     1     2     3

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

ans = 1×7

     5     6     7     1     2     3     4

Shift 1-D Signal

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

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

fs = 100;               % sampling frequency
t = 0:(1/fs):(10-1/fs); % time vector
S = cos(2*pi*15*t);
n = length(S);
X = fft(S);
f = (0:n-1)*(fs/n);     %frequency range
power = abs(X).^2/n;    %power
plot(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 range
powershift = abs(Y).^2/n;     % zero-centered power
plot(fshift,powershift)

Shift Signals in Matrix

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 matrix A whose rows represent two 1-D signals, and compute the Fourier transform of each signal. Plot the power for each signal.

fs = 100;               % sampling frequency
t = 0:(1/fs):(10-1/fs); % time vector
S1 = 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 range
power = abs(X).^2/n;    % power
plot(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 range
powershift = abs(Y).^2/n;     % zero-centered power
plot(fshift,powershift(1,:),fshift,powershift(2,:))

Input Arguments

X — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, a matrix, or a multidimensional array.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
Complex Number Support: Yes

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then fftshift swaps along all dimensions.

• Consider an input matrix Xc. The operation fftshift(Xc,1) swaps halves of each column of Xc.

  

• Consider a matrix Xr. The operation fftshift(Xr,2) swaps halves of each row of Xr.

  

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).