Title :
On the Fixed-Point Accuracy Analysis of FFT Algorithms
Author :
Chang, Wei-Hsin ; Nguyen, Truong Q.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California San Diego, La Jolla, CA
Abstract :
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.
Keywords :
fast Fourier transforms; fixed point arithmetic; matrix algebra; quantisation (signal); signal processing; FFT algorithms; arithmetic quantization errors; decimation-in-frequency configuration; decimation-in-time configuration; digital signal processing; error propagation model; fast Fourier transform algorithms; fixed-point accuracy analysis; matrix representation; quantization loss; radix-2 DIT FFT algorithm; rounding effect; signal-to-quantization-noise ratio; Algorithm design and analysis; Digital video broadcasting; Discrete Fourier transforms; Error analysis; Fast Fourier transforms; Fixed-point arithmetic; Hardware; Performance analysis; Quantization; Signal processing algorithms; Decimation-in-frequency (DIF); Fast Fourier transform (FFT); decimation-in-time (DIT); quantization loss analysis;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2008.924637
