On the design of the FFT Butterfly Units

Abstract

In this paper, efficient designs of the Fast Fourier Transform (FFT) Decimation-in-Time (DIT), radix-2, Butterfly Unit are proposed. Several techniques are incorporated in order to achieve higher performance. The operations are fused by keeping the intermediate variables in Carry-Save format. Besides of the conventional, the Gauss complex multiplication algorithm is also explored. Considered that the twiddle factors cosϕ, sinϕ used in FFT algorithm are constant numbers, we apply to them a special NR4SD encoding scheme with the following sets of digit values: {−2, −1, 0, +1}. Finally, to increase the operation speed, one level of pipelining is introduced in all designs. We implement four designs: one conventional and three new Butterfly Units. In all cases, the proposed three schemes are superior in terms of operation speed, area and power, compared to the conventional.