On a wideband fast fourier transform using piecewise linear approximations: application to a radio telescope spectrometer

Authors:
Hiroki Nakahara;Hiroyuki Nakanishi;Tsutomu Sasao
Affiliations:
Faculty of Engineering, Kagoshima University, Japan;Faculty of Science, Kagoshima University, Japan;Department of Creative Informatics, Kyushu Institute of Technology, Japan
Venue:
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Year:
2012

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Abstract

In a radio telescope, a spectrometer analyzes radio frequency (RF) received from celestial objects at the frequency domain by performing a fast fourier transform (FFT). In radio astronomy, the number of points for the FFT is larger than that for the general purpose one. Thus, in a conventional design, the twiddle factor memory becomes too large to implement. In this paper, we realize a twiddle factor by a piecewise linear approximation circuit consisting of a small memory, a multiplier, an adder, and a small logic circuit. We analyze the approximation error for the piecewise liner approximation circuit for the twiddle factor part. We implemented the 230 points FFT by the R2kFFT with the piecewise linear approximation circuits. Compared with the SETI spectrometer for 227-FFT, the eight parallelized proposed circuit for 227-FFT is 41.66 times faster, and that for 230-FFT is 5.20 times faster. Compared with the GPU-based spectrometer for 227-FFT, the proposed one is 8.75 times faster and dissipates lower power.