Architectures for multiplierless fast Fourier transform hardware implementation in VLSI

This paper presents a novel processor for the implementation of multiplierless FFT's in VLSI. The arithmetic scheme is specially tailored for the simple binary coefficients used for these FFT's, which make multiplication trivial. (The class of coefficients dealt with are those that have a maximum of 2 nonzero digits; i.e., sum of 2 integers powers of 2 with each power in the range 0-4.) A single chip processing element for a 4-point DFT (for a radix 4 FFT) with an execution time of 400 ns using a 10 MHz clock has been realized. The chip has an estimated maximum gate count of 11 000 and pin count of 85. It has the capability of achieving a 40 MHz throughput rate for a 1024-point FFT using 20 processing IC's. The use of the 4-point chip to implement higher radix algorithms and various other issues are discussed.