Asymptotic Performance of Delayed Delta Coding with Single and Double Integration

A study of the asymptotic performance of delta coding with delayed decision is presented for the cases of first and second order integration assuming a stationary, bandlimited Gaussian source. The resulting signal-to-distortion-ratio serves as an upper bound for any delayed (multipath) decision scheme provided that the sampling rate exceeds the Nyquist rate by a factor greater than about two. The analysis shows that the improvement offered by delayed encoding relative to ordinary delta modulation has its basic origin in diminished overload distortion. Some insight is given into how the improvement is related to the decoding filter. Finally, numerical results are given for some sources with speech-like spectra