On the Fixed-Point Accuracy Analysis of FFT Algorithms

In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier transform (FFT) algorithms. A matrix representation of error propagation model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2008-10, Vol.56 (10), p.4673-4682
Main Authors: Wei-Hsin Chang, Nguyen, T.Q.
Format: Article
Language:English
Subjects:
Accuracy
Algorithm design and analysis
Algorithms
Applied sciences
Arithmetic
Decimation-in-frequency (DIF)
decimation-in-time (DIT)
Digital video broadcasting
Discrete Fourier transforms
Error analysis
Exact sciences and technology
Fast Fourier transform (FFT)
Fast Fourier transforms
Fixed points (mathematics)
Fixed-point arithmetic
Fourier transforms
Hardware
Information, signal and communications theory
Mathematical analysis
Matrix representation
Miscellaneous
Performance analysis
Quantization
quantization loss analysis
Sampling, quantization
Signal and communications theory
Signal processing
Signal processing algorithms
Telecommunications and information theory
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Summary:In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier transform (FFT) algorithms. A matrix representation of error propagation model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to the arithmetic quantization errors is derived to compare the performance with decimation-in-time (DIT) and decimation-in-frequency (DIF) configurations. From the simulation results, the radix-2 DIT FFT algorithm has better accuracy in term of signal-to-quantization-noise ratio (SQNR). Based on the results, a simple criterion of wordlength optimization is proposed to yield comparable accuracy with fewer bit budget.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.924637