Low-Complexity Constant Multiplication Based on Trigonometric Identities with Applications to FFTs

Fahad QURESHI  Oscar GUSTAFSSON  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E94-A   No.11   pp.2361-2368
Publication Date: 2011/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.2361
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
complex multiplier,  FFT,  constant multiplication,  shift-and-add multiplication,  

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Summary: 
In this work we consider optimized twiddle factor multipliers based on shift-and-add-multiplication. We propose a low-complexity structure for twiddle factors with a resolution of 32 points. Furthermore, we propose a slightly modified version of a previously reported multiplier for a resolution of 16 points with lower round-off noise. For completeness we also include results on optimal coefficients for eight-points resolution. We perform finite word length analysis for both coefficients and round-off errors and derive optimized coefficients with minimum complexity for varying requirements.