Comparative Analysis of Alternatives of Rotators in Single Path Delay Feedback FFT architecturen

Abstract

Rotators are an essential part of fast Fourier transform (FFT) butterfly architecture. It defines the overall complexity of the FFT computation between the stages in the signal flow graph of the single path delay feedback FFT architecture. Rotations are basically multiplication by a complex number having magnitude equal to one, therefore only the phase of the multiplicand is changed. In 16 point radix 2 Single path delay feedback (SDF) FFT the number of stages is four and every stage the rotations are involved. Increasing the radix to 4, reduces the number of stages and consequently the rotation between stages is also reduced but it increases the complexity of the architecture. Different realizations of rotations exist like general complex multiplier, Coordinate rotation digital computer (CORDIC) and the constant multiplication. These techniques use shift and add based methods to realize the rotations. This paper compares the different alternatives of rotations for different angles in terms of the number of adders as a function of bits.