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fftshift

Shift zero-frequency component to center of spectrum

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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.

example

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.

example

Examples

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Open Live Script

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
Open Live Script

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)

Figure contains an axes object. The axes object contains an object of type line.

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)

Figure contains an axes object. The axes object contains an object of type line.

Open Live Script

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,:))

Figure contains an axes object. The axes object contains 2 objects of type line.

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,:))

Figure contains an axes object. The axes object contains 2 objects of type line.

Input Arguments

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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

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.

    fftshift(Xc,1) column-wise operation

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

    fftshift(Xr,2) row-wise operation

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™.

Version History

Introduced before R2006a

See Also

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