A new memory reference reduction method for FFT implementation on DSP

Memory reference in digital signal processors (DSP) is among the most costly operations due to its long latency and substantial power consumption. In this paper, we present a new method to minimize memory references due to twiddle factors for implementing any existing fast Fourier transform (FFT) algorithms on DSP processors. The new method takes advantage of previously proposed twiddle factor reduction method (TFRM) and twiddle-factor-based butterfly grouping method (TFBBGM). It can compute two butterflies in one stage of any FFT diagram by loading only one twiddle-factor. Further memory reference reduction is done by computing butterflies with the same twiddle factor at the same time in different stages of the FFT diagram. We have applied the new method to implement radix-2 DIT FFT algorithm on TI TMS320C64x DSP. While using only 50% memory space for storing twiddle factors compared to the conventional DIT FFT implementation, the new method achieves an average reduction in the number of memory references by 79% for accessing the twiddle factors, and 17.5% reduction in the number of clock cycles.

[1]  P. Duhamel,et al.  `Split radix' FFT algorithm , 1984 .

[2]  R. Singleton.  An algorithm for computing the mixed radix fast Fourier transform , 1969 .

[3]  Bevan M. Baas,et al.  A low-power, high-performance, 1024-point FFT processor , 1999, IEEE J. Solid State Circuits.

[4]  Yingtao Jiang,et al.  Twiddle-factor-based FFT algorithm with reduced memory access , 2002, Proceedings 16th International Parallel and Distributed Processing Symposium.

[5]  T. Parks,et al.  A prime factor FFT algorithm using high-speed convolution , 1977 .

[6]  G. Bergland,et al.  A radix-eight fast Fourier transform subroutine for real-valued series , 1969 .

[7]  Annamária R. Várkonyi-Kóczy,et al.  A recursive fast Fourier transformation algorithm , 1995 .

[8]  Ali Saidi,et al.  Decimation-in-time-frequency FFT algorithm , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[9]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[10]  D. Takahashi,et al.  An extended split-radix FFT algorithm , 2001, IEEE Signal Processing Letters.

[11]  S. Winograd.  On computing the Discrete Fourier Transform. , 1976, Proceedings of the National Academy of Sciences of the United States of America.