Intel® Integrated Performance Primitives Developer Guide and Reference

ID 790148
Date 11/07/2023
Public

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Fourier Transforms

Intel IPP functions that compute FFT and DFT can process both real and complex images. Function flavors operating on real data are distinguished by R suffix present in function-specific modifier of their full name, whereas complex flavors' names include C suffix (see Function Naming).

The results of computing the Fourier transform can be normalized by specifying the appropriate value of flag argument for context initialization. This parameter sets up a pair of matched normalization factors to be used in forward and inverse transforms as listed in the following table:

Normalization Factors for Fourier Transform Results
Value of flag Argument Normalization Factors
Forward Transform Inverse Transform
IPP_FFT_DIV_FWD_BY_N 1/MN 1
IPP_FFT_DIV_INV_BY_N 1 1/MN
IPP_FFT_DIV_BY_SQRTN 1/sqrt(MN) 1/sqrt(MN)
IPP_FFT_NODIV_BY_ANY 1 1

In this table, N and M denote the length of Fourier transform in the x- and y-directions, respectively (or, equivalently, the number of columns and rows in the 2D array being transformed).

For the FFT, these lengths must be integer powers of 2, that is N=2orderX, M=2orderY, where power exponentsare known as order of FFT.

For the DFT, N and M can take on arbitrary integer non-negative values.