Intel® Integrated Performance Primitives (Intel® IPP) Developer Guide and Reference

ID 790148
Date 3/22/2024
Public
Document Table of Contents

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.