Algorithm - 9.1 English

PG109 Fast Fourier Transform LogiCORE IP Product Guide

Document ID
PG109
Release Date
2022-05-04
Version
9.1 English

The FFT core uses the Radix-4 and Radix-2 decompositions for computing the DFT. For Burst I/O architectures, the decimation-in-time (DIT) method is used, while the decimation-in-frequency (DIF) method is used for the Pipelined Streaming I/O architecture. When using Radix-4 decomposition, the N -point FFT consists of log 4 (N) stages, with each stage containing N/4 Radix-4 butterflies. Point sizes that are not a power of 4 need an extra Radix-2 stage for combining data. An N -point FFT using Radix-2 decomposition has log 2 ( N) stages, with each stage containing N/2 Radix-2 butterflies.

The inverse FFT (IFFT) is computed by conjugating the phase factors of the corresponding forward FFT. The FFT core does not implement the 1/N scaling for inverse FFT. The scaling is therefore as per forward FFT, simply with conjugated phase factors (twiddle factors).