Analysis of complex LNS FFTs

The complex-logarithmic number system (CLNS), which represents each complex point in log/polar coordinates, may be practical to implement the fast Fourier transform (FFT). The roots of unity needed by the FFT have exact representations in CLNS and do not require a ROM. We present an error analysis and simulation results for a radix-two FFT that compares a rectangular fixed-point representation of complex numbers to the CLNS. We observe that the CLNS saves 9-12 bits in word-size for 256-1024 point FFTs compared to the fixed-point number system while producing comparable accuracy.