Floating point error bound in the prime factor FFT

The prime factor FFT <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 MSE in the PF FFT assuming finite precision fixed point arithmetic. In this paper we derive a bound on the MSE in the PF FFT assuming floating point arithmetic. In the course of the derivation an expression for the actual MSE is also presented, but is seen to be too complicated to be of practical use.