On a Wideband Fast Fourier Transform Using Piecewise Linear Approximations: Application to a Radio Telescope Spectrometer

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 R2^k FFT 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.