Roundoff error analysis of the discrete Wigner distribution using fixed-point arithmetic

The authors investigate the roundoff noise in a fixed-point implementation of a discrete Wigner distribution (DWD) algorithm. The output noise-to-signal ratio (NSR) is derived using a statistical approach based on certain assumptions about the input signal. The expression for noise-to-signal ratio indicates that for each added stage in the DWD implementation, the fixed-point wordlength should be increased by one bit to keep the noise-to-signal ratio unchanged. The theoretical result has been validated by computer simulations using similar input data. It is found that doubling the length of the DWD increases the NSR by approximately 6 dB