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Power Spectral Density of the Quantization Noise in Block-Floating-Point FFT

Authors:
Gil Naveh

Keywords: BFP; Fixed Point; DIT; DIF; PSD; SQNR

Abstract:
The Power Spectral Density (PSD) of quantization noise in fixed-point Fast Fourier Transform (FFT) implementations is traditionally assumed to be white. However, this assumption often fails in practical hardware, particularly in CPUs and DSPs employing Block-Floating-Point (BFP) arithmetic. Due to hardware efficiency constraints, these processors frequently utilize Rounding-Half-Up (RHU), a native operation that introduces an inherent statistical bias. Throughout the BFP-FFT stages, these cumulative biases propagate to the output, coloring the quantization noise and creating frequency-dependent power variations. This correlation can severely degrade performance in sensitive applications such as OFDM modems and high-fidelity audio codecs. This paper analyzes the impact of rounding bias on the noise spectrum and provides a comparative study of Decimation-In-Time (DIT) vs. Decimation-In-Frequency (DIF) topologies. We demonstrate that the DIF architecture is significantly more sensitive to this bias. Finally, we present three mitigation schemes, showing that convergent rounding, when supported by the hardware, effectively restores the output noise to a near-white spectral state.

Pages: 14 to 19

Copyright: Copyright (c) IARIA, 2026

Publication date: March 8, 2026

Published in: conference

ISSN: 2519-8432

ISBN: 978-1-68558-360-6

Location: Valencia, Spain

Dates: from March 8, 2026 to March 12, 2026