Quantising noise spectra

Bennett´s approximation for the spectrum of quantising noise is both numerically accurate and computationally economical, but apparently does not correspond to the physical mechanism of intermodulation producing the noise. On the other hand Velichkin´s approach reveals this structure, but Robertson´s computation of his formula becomes rather expensive for quantisers with more than 16 levels. In this paper we derive Bennett´s result by a new route, starting from the noise analysis of Blachman. We show that Velichkin´s intermodulation series has a `line-structure¿ which, when exploited for approximation leads to Bennett´s B series. Bennett´ s approximation may now be reinterpreted as a genuine intermodulation series in which low-order terms are absent, and we show how this explains the experimentally observed flatness of quantising noise spectra for arbitrary input spectra and for high sampling rates. We also present some experimental results which indicate that the noise/signal ratio defined in terms of Blachman´s analysis is a better estimate of system performance than the conventional meansquared-error analysis in cases where the quantiser is not globally linear, as for instance when compandor and expander are mismatched.