ifft2

2-D inverse fast Fourier transform

Syntax

X = ifft2(Y)

X = ifft2(Y,m,n)

X = ifft2(___,symflag)

Description

X = ifft2(Y) returns the two-dimensional discrete inverse Fourier transform of a matrix using a fast Fourier transform algorithm. If Y is a multidimensional array, then ifft2 takes the 2-D inverse transform of each dimension higher than 2. The output X is the same size as Y.

example

X = ifft2(Y,m,n) truncates Y or pads Y with trailing zeros to form an m-by-n matrix before computing the inverse transform. X is also m-by-n. If Y is a multidimensional array, then ifft2 shapes the first two dimensions of Y according to m and n.

example

X = ifft2(___,symflag) specifies the symmetry of Y. For example, ifft2(Y,'symmetric') treats Y as conjugate symmetric.

Examples

collapse all

2-D Inverse Transform of Matrix

Open Live Script

You can use the ifft2 function to convert 2-D signals sampled in frequency to signals sampled in time or space. The ifft2 function also allows you to control the size of the transform.

Create a 3-by-3 matrix and compute its Fourier transform.

X = magic(3)

X = 3×3

     8     1     6
     3     5     7
     4     9     2

Y = fft2(X)

Y = 3×3 complex

  45.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i  13.5000 + 7.7942i   0.0000 - 5.1962i
   0.0000 - 0.0000i   0.0000 + 5.1962i  13.5000 - 7.7942i

Take the inverse transform of Y, which is the same as the original matrix X, up to round-off error.

ifft2(Y)

ans = 3×3

    8.0000    1.0000    6.0000
    3.0000    5.0000    7.0000
    4.0000    9.0000    2.0000

Pad both dimensions of Y with trailing zeros so that the transform has size 8-by-8.

Z = ifft2(Y,8,8);
size(Z)

ans = 1×2

     8     8

Conjugate Symmetric Matrix

Open Live Script

For nearly conjugate symmetric matrices, you can compute the inverse Fourier transform faster by specifying the 'symmetric' option, which also ensures that the output is real.

Compute the 2-D inverse Fourier transform of a nearly conjugate symmetric matrix.

Y = [3+1e-15*i 5;
     5 3];
X = ifft2(Y,'symmetric')

Input Arguments

collapse all

`Y` — Input array
matrix | multidimensional array

Input array, specified as a matrix or a multidimensional array. If Y is of type single, then ifft2 natively computes in single precision, and X is also of type single. Otherwise, X is returned as type double.

`m` — Number of inverse transform rows
positive integer scalar

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

`n` — Number of inverse transform columns
positive integer scalar

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

`symflag` — Symmetry type
`'nonsymmetric'` (default) | `'symmetric'`

Symmetry type, specified as 'nonsymmetric' or 'symmetric'. When Y is not exactly conjugate symmetric due to round-off error, ifft2(Y,'symmetric') treats Y as if it were conjugate symmetric. For more information on conjugate symmetry, see Algorithms.

More About

collapse all

2-D Inverse Fourier Transform

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

$X_{p, q} = \frac{1}{m} \sum_{j = 1}^{m} \frac{1}{n} \sum_{k = 1}^{n} ω_{m}^{(j - 1) (p - 1)} ω_{n}^{(k - 1) (q - 1)} Y_{j, k}$

ω_m and ω_n are complex roots of unity:

$\begin{array}{l} ω_{m} = e^{2 π i / m} \\ ω_{n} = e^{2 π i / n} \end{array}$

i is the imaginary unit. p runs from 1 to m and q runs from 1 to n.

Algorithms

The ifft2 function tests whether the vectors in a matrix Y are conjugate symmetric in both dimensions. A vector v is conjugate symmetric when the ith element satisfies v(i) = conj(v([1,end:-1:2])). If the vectors in Y are conjugate symmetric in both dimensions, then the inverse transform computation is faster and the output is real.

Extended Capabilities

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

Usage notes and limitations:

Symmetry type 'symmetric' is not supported.
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 Support Package for ARM Cortex-A Processors). 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 Support Package for ARM Cortex-A Processors).
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 Support Package for ARM Cortex-M Processors). 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 Support Package for ARM Cortex-M Processors).

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

Usage notes and limitations:

Symmetry type 'symmetric' is not supported.

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

Usage notes and limitations:

Unless symflag is 'symmetric', the output is always complex even if all imaginary parts are zero.

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).

Documentation

ifft2

Syntax

Description

Examples

2-D Inverse Transform of Matrix

Conjugate Symmetric Matrix

Input Arguments

`Y` — Input array
matrix | multidimensional array

`m` — Number of inverse transform rows
positive integer scalar

`n` — Number of inverse transform columns
positive integer scalar

`symflag` — Symmetry type
`'nonsymmetric'` (default) | `'symmetric'`

More About

2-D Inverse Fourier Transform

Algorithms

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™.

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

See Also

MATLAB Documentation

Support

Documentation

ifft2

Syntax

Description

Examples

2-D Inverse Transform of Matrix

Conjugate Symmetric Matrix

Input Arguments

Y — Input array matrix | multidimensional array

m — Number of inverse transform rows positive integer scalar

n — Number of inverse transform columns positive integer scalar

symflag — Symmetry type 'nonsymmetric' (default) | 'symmetric'

More About

2-D Inverse Fourier Transform

Algorithms

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™.

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

See Also

MATLAB Documentation

Support

`Y` — Input array
matrix | multidimensional array

`m` — Number of inverse transform rows
positive integer scalar

`n` — Number of inverse transform columns
positive integer scalar

`symflag` — Symmetry type
`'nonsymmetric'` (default) | `'symmetric'`

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™.

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