Floating point roundoff error in the prime factor FFT

Abstract

The prime factor fast Fourier transform (PF FFT), developed by Kolba and Parks, makes use of recent computational complexity results by Winograd to compute the DFT with a fewer number of multiplications than that required by the FFT. Patterson and McClellan have derived an expression for the mean squared error (MSE) in the PF FFT, assuming finite precision fixed point arithmetic. In this paper, we derive an expression for the MSE in the PF FFT, assuming floating point arithmetic. This expression is quite complicated, so an upper bound on the MSE is also derived which is easier to compute. Simulation results are presented comparing the error in the PF FFT with both the derived bound and the error observed in a radix-2 FFT.