A Saturation Analysis of
D. Stacey, Richard L. Frost, Gene A. Ware · 1996
Error spectrum shaping (ESS) quantizers are ana- lyzed in the context of realistic reconstruction filters and noo probability of saturation. Conditions for stable operation are derived, and a suboptimal but effective and computationally efficient design method is proposed. Excellent agreement is ob- tained between the analysis and simulations. Even under these more stringent constraints, ESS quantizers are shown to achieve significant signal-to-quantization-noise ratio (SQNR) gains when quantizing oversampled Gaussian sources. They gave a solution for the optimal finite-impulse-response (FIR) feedback filter and characterized the improvement in SQNR as a function of filter length. Their analysis predicts that the distortion of the reconstructed signal will decrease indefinitely as length is increased. However, this result is nonphysical and overestimates the SQNR gains obtainable with any given realizable reconstruction filter. This is because the energy of the impulse response of the optimal feedback filter increases rapidly with increasing length and leads to violations of both simplifying assumptions mentioned above. Assumption 1 is violated because the error power in the guardband gows too large to be adequately removed by the particular reconstruction filter. Assumption 2 is violated because the large feedback signal will cause frequent quantizer saturation. These effects are not significant when the feedback filter has only a few taps, which perhaps explains why previous researchers, concerned principally with second order IIR filter