FFTn

N-D快速傅立叶变换

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Syntax

Y = fftn(X)

Y = fftn(X,sz)

Description

Y = fftn(X)returns the多维傅立叶变换一个N-D array using a fast Fourier transform algorithm. The N-D transform is equivalent to computing the 1-D transform along each dimension ofX。输出Y大小与X。

example

Y = fftn(X,sz)truncatesXor padsXwith trailing zeros before taking the transform according to the elements of the vectorsz。Each element ofszdefines the length of the corresponding transform dimensions. For example, ifXis a 5-by-5-by-5 array, thenY = fftn(X,[8 8 8])pads each dimension with zeros resulting in an 8-by-8-by-8 transformY。

Examples

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3-D变换

打开实时脚本

You can use theFFTnfunction to compute a 1-D fast Fourier transform in each dimension of a multidimensional array.

Create a 3-D signalX。的大小Xis 20-by-20-by-20.

x = (1:20)'; y = 1:20; z = reshape(1:20,[1 1 20]); X = cos(2*pi*0.01*x) + sin(2*pi*0.02*y) + cos(2*pi*0.03*z);

Compute the 3-D Fourier transform of the signal, which is also a 20-by-20-by-20 array.

y = fftn（x）;

PadXwith zeros to compute a 32-by-32-by-32 transform.

m = nextpow2(20); Y = fftn(X,[2^m 2^m 2^m]); size(Y)

ans =1×332 32 32

Input Arguments

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`X`—输入数组
matrix|多维阵列

输入数组，指定为矩阵或多维数组。如果Xis of typesingle, thenFFTn本地计算以单个精度计算，并且Yis also of typesingle。否则，Yis returned as typedouble。

`sz`—Length of transform dimensions
vector of positive integers

Length of the transform dimensions, specified as a vector of positive integers. The elements ofszcorrespond to the transformation lengths of the corresponding dimensions ofX。length(sz)must be at leastndims(X)。

More About

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N-D Fourier Transform

离散的傅立叶变换Y一个N-d数组Xis defined as

$Y_{p_{1}, p_{2}, 。。。, p_{N}} = \sum_{j_{1} = 0}^{m_{1} - 1} ω_{m_{1}}^{p_{1} j_{1}} \sum_{j_{2} = 0}^{m_{2} - 1} ω_{m_{2}}^{p_{2} j_{2}} 。。。 \sum_{j_{N}}^{m_{N} - 1} ω_{m_{N}}^{p_{N} j_{N}} X_{j_{1}, j_{2}, 。。。, j_{N}} 。$

Each dimension has lengthm_kfork= 1,2,...,N，和 $ω_{m_{k}} = e^{- 2 π i / m_{k}}$ 是统一的复杂根源iis the imaginary unit.

Extended Capabilities

C/C++ Code Generation
使用MATLAB®CODER™生成C和C ++代码。

Usage notes and limitations:

Thesz参数必须具有固定的大小。
对于MEX输出，MATLAB^®Coder™使用MATLAB用于FFT算法的库。对于独立的C/C ++代码，默认情况下，代码生成器生成用于FFT算法的代码，而不是生成FFT库调用。要生成针对特定安装的FFTW库的呼叫，请提供FFT库回调类。有关FFT库回调类的更多信息，请参阅coder.fftw.StandaloneFFTW3Interface(MATLAB Coder)。
For simulation of aMATLAB功能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, seecoder.fftw.StandaloneFFTW3Interface(MATLAB Coder)。
Using the Code Replacement Library (CRL), you can generate optimized code that runs onARM^®皮质^®-A processors with Neon extension. To generate this optimized code, you must install the嵌入式编码器^®Support Package for ARM Cortex-A Processors（ARM Cortex-A处理器金宝app的嵌入式编码器支持包）。The generated code for手臂皮层-A uses the Ne10 library. For more information, seeMATLAB功能支持ARM Cortex-A处理器的NE10条件金宝app（ARM Cortex-A处理器金宝app的嵌入式编码器支持包）。
Using the Code Replacement Library (CRL), you can generate optimized code that runs on手臂皮层-M processors. To generate this optimized code, you must install theARM Cortex-M处理器金宝app的嵌入式编码器支持包（ARM Cortex-M处理器金宝app的嵌入式编码器支持包）。The generated code for手臂皮层-M使用CMSIS库。有关更多信息，请参阅CMSIS Conditions for MATLAB Functions to Support ARM Cortex-M Processors（ARM Cortex-M处理器金宝app的嵌入式编码器支持包）。

GPU Code Generation
使用GPU CODER™为NVIDIA®GPU生成CUDA®代码。

Usage notes and limitations:

Thesz参数必须具有固定的大小。

Thread-Based Environment
Run code in the background using MATLAB®`背景池`or accelerate code with Parallel Computing Toolbox™`螺纹池`。

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment。

GPU Arrays
使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

Usage notes and limitations:

输出Y即使所有虚构零件为零，也总是复杂的。

有关更多信息，请参阅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™.

此功能完全支持分布式数组。金宝app有关更多信息，请参阅运行具有分布式数组的MATLAB功能(Parallel Computing Toolbox)。

Version History

在R2006a之前引入

FFTn

Syntax

Description

Examples

3-D变换

Input Arguments

X—输入数组matrix|多维阵列

sz—Length of transform dimensionsvector of positive integers

More About

N-D Fourier Transform

Extended Capabilities

C/C++ Code Generation使用MATLAB®CODER™生成C和C ++代码。

GPU Code Generation使用GPU CODER™为NVIDIA®GPU生成CUDA®代码。

Thread-Based EnvironmentRun code in the background using MATLAB®背景池or accelerate code with Parallel Computing Toolbox™螺纹池。

GPU Arrays使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

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

Version History

See Also

`X`—输入数组
matrix|多维阵列

`sz`—Length of transform dimensions
vector of positive integers

C/C++ Code Generation
使用MATLAB®CODER™生成C和C ++代码。

GPU Code Generation
使用GPU CODER™为NVIDIA®GPU生成CUDA®代码。

Thread-Based Environment
Run code in the background using MATLAB®`背景池`or accelerate code with Parallel Computing Toolbox™`螺纹池`。

GPU Arrays
使用并行计算工具箱™在图形处理单元（GPU）上运行加速代码。

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