fft2 - 2-D fast Fourier transform - MATLAB (original) (raw)

2-D fast Fourier transform

Syntax

Description

Y = fft2([X](#bvhck3f-X)) returns the two-dimensional Fourier transform of a matrix X using a fast Fourier transform algorithm, which is equivalent to computingfft(fft(X).').'.

When X is a multidimensional array, fft2 computes the 2-D Fourier transform on the first two dimensions of each subarray ofX that can be treated as a 2-D matrix for dimensions higher than 2. For example, if X is anm-by-n-by-1-by-2 array, then Y(:,:,1,1) = fft2(X(:,:,1,1)) and Y(:,:,1,2) = fft2(X(:,:,1,2)). The output Y is the same size as X.

example

Y = fft2([X](#bvhck3f-X),[m](#bvhck3f-m),[n](#bvhck3f-n)) truncates X or pads X with trailing zeros to form an m-by-n matrix before computing the transform. If X is a matrix, then Y is anm-by-n matrix. If X is a multidimensional array, then fft2 shapes the first two dimensions of X according to m andn.

example

Examples

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The 2-D Fourier transform is useful for processing 2-D signals and other 2-D data such as images.

Create and plot 2-D data with repeated blocks.

P = peaks(20); X = repmat(P,[5 10]); imagesc(X)

Compute the 2-D Fourier transform of the data. Shift the zero-frequency component to the center of the output, and plot the resulting 100-by-200 matrix, which is the same size as X.

Y = fft2(X); imagesc(abs(fftshift(Y)))

Pad X with zeros to compute a 128-by-256 transform.

Y = fft2(X,2^nextpow2(100),2^nextpow2(200)); imagesc(abs(fftshift(Y)));

Input Arguments

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Input array, specified as a matrix or a multidimensional array. If X is of type single, then fft2 natively computes in single precision, and Y is also of type single. Otherwise, Y is returned as type double.

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

Number of transform rows, specified as a positive integer scalar.

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

Number of transform columns, specified as a positive integer scalar.

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

More About

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This formula defines the discrete Fourier transform Y of an _m_-by-n matrix X:

ωm and ωn are complex roots of unity:

i is the imaginary unit. p and j are indices that run from 0 to _m_–1, and q and k are indices that run from 0 to _n_–1. This formula shifts the indices for X and Y by 1 to reflect matrix indices in MATLAB®.

Extended Capabilities

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Usage notes and limitations:

• For MEX output, MATLAB Coder™ uses the library that MATLAB uses for FFT algorithms. For standalone C/C++ code, by default, the code generator produces code for FFT algorithms instead of producing FFT library calls. To generate calls to a specific installed FFTW library, provide an FFT library callback class. For more information about an FFT library callback class, see coder.fftw.StandaloneFFTW3Interface (MATLAB Coder).
• For simulation of a MATLAB Function block, the simulation software uses the library that MATLAB uses for FFT algorithms. For C/C++ code generation, by default, the code generator produces code for FFT algorithms instead of producing FFT library calls. To generate calls to a specific installed FFTW library, provide an FFT library callback class. For more information about an FFT library callback class, see coder.fftw.StandaloneFFTW3Interface (MATLAB Coder).
• Using the Code Replacement Library (CRL), you can generate optimized code that runs on ARM® Cortex®-A processors with Neon extension. To generate this optimized code, you must install the Embedded Coder® Support Package for ARM Cortex-A Processors (Embedded Coder). The generated code for ARM Cortex-A uses the Ne10 library. For more information, see Ne10 Conditions for MATLAB Functions to Support ARM Cortex-A Processors (Embedded Coder).
• Using the Code Replacement Library (CRL), you can generate optimized code that runs on ARM Cortex-M processors. To generate this optimized code, you must install the Embedded Coder Support Package for ARM Cortex-M Processors (Embedded Coder). The generated code for ARM Cortex-M uses the CMSIS library. For more information, see CMSIS Conditions for MATLAB Functions to Support ARM Cortex-M Processors (Embedded Coder).

The fft2 function supports GPU array input with these usage notes and limitations:

• The output Y is always complex even if all the imaginary parts are zero.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a