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Finite Word Length Effect in Practical Block-Floating-Point FFT

Authors:
Gil Naveh

Keywords: Block Floating Point; Fixed Point; DIT; SQNR

Abstract:
Fixed-Point FFT implementation is very sensitive to finite-word-length-effects due to the large quantization noise that is being accumulated throughout the FFT stages. In FFT implementations on fixed register size processors like CPUs and DSPs, Block-Floating-Point (BFP) is a well-known scheme for controlling the tradeoffs between the fixed-point register size and the resultant accuracy. The performance of the ideal BFP FFT, in terms of the output Signal to Quantization Noise Ratio (SQNR), has been investigated in depth. However, ideal BFP-FFT suffers from implementation complexity, and especially non-deterministic latency. This is caused by the inherent mechanism that requires to re-calculate an entire FFT stage if one of the stage’s output overflows. Because of this, most of the implementations are of a more practical variant for the BFP-FFT that does guarantee fixed latency. This, however, comes on the expense of reduced accuracy (degraded SQNR). In this paper, we derive the SQNR formulas for the practical BFP-FFT for radix-2 and radix-4 Cooley-Tukey Decimation-In-Time (DIT) FFTs. The derived model is compared to computer simulations and found highly accurate (less than 0.2dB difference). We use the derived model to compare the SQNR performance of the practical algorithm to the ideal one and show a 6-14dB penalty cost for guaranteeing fixed latency implementation.

Pages: 33 to 39

Copyright: Copyright (c) IARIA, 2025

Publication date: March 9, 2025

Published in: conference

ISSN: 2519-8432

ISBN: 978-1-68558-245-6

Location: Lisbon, Portugal

Dates: from March 9, 2025 to March 13, 2025