Accumulation of coefficient roundoff error in fast Fourier transforms implemented with logarithmic number system

Abstract

When a fast Fourier transform (FFT) is implemented on a digital computer or with special-purpose hardware, quantization errors will arise due to finite word lengths in the digital system. This correspondence presents an analysis of error accumulation due to coefficient rounding in the FFT implemented with a logarithmic number system. The theoretical result of the coefficient roundoff error analysis is verified by computer simulations. The results indicate that the FFT implemented with the logarithmic number system provides better signal-to-noise performance than that implemented with a fixed-point or floating-point number system.