Implementation of 'multiply-add' FFT algorithms for complex and real data sequences

摘要

Multiply-add FFT algorithms are FFT algorithms that take advantage of computer architectures with a multiply-add feature. Various FFT algorithms can be implemented on this type of architecture to give the multiplications for free. In the present work, some of these FFT algorithms are reviewed: the split-radix FFT algorithm for 2/sup k/ transform sizes, the multiplicative algorithms for prime transform sizes, and the prime factor algorithm for transform sizes with relatively prime factors. Both complex and real data sequences are considered, and operational counts are evaluated in terms of total floating-point operations. Tensor product formulation is used throughout for producing variants of algorithms matching to computer architecture.