An FFT Circuit for a Spectrometer of a Radio Telescope using the Nested RNS including the Constant Division

Abstract

A radio telescope analyzes radio frequency (RF) received from celestial objects. It consists of an antenna, a receiver, and a spectrometer. The spectrometer converts the time domain into the frequency domain by an FFT operation. This paper applies an FFT circuit based on nested residue number system (NRNS), which recursively decompose the RNS. It can decompose the MAC unit into circuits with small sizes. In the FFT using the NRNS, a MAC unit is decomposed into 4-bit ones realized by look-up tables of the FPGA. Also, to realize the scaling (truncation) circuit, we propose a constant division algorithm on the FPGA. The truncation is realized by the division of a dynamic range for a subset of moduli. We implemented the proposed NRNS FFT on the Xilinx Inc. Virtex 6 FPGA. Compared with a Xilinx Inc. binary FFT library, although the number of block RAMs (BRAMs) was increased by 38%, in the RNS FFT, the number of LUTs was decreased by 42-45% and the maximum clock frequency was increased by 38-74%. With this technique, we successfully implemented an FFT that satisfied the required size and speed specifications on an available FPGA, since the excessive number of LUTs was the bottleneck of the binary FFT.