On optimal perfect reconstruction feedback quantizers

Milan S. Derpich, Eduardo I. Silva, Daniel E. Quevedo, Graham C. Goodwin

Research output: Contribution to journalArticle

31 Citations (Scopus)


This paper presents novel results on perfect reconstruction feedback quantizers (PRFQs), i.e., noise-shaping, predictive and sigma-delta A/D converters whose signal transfer function is unity. Our analysis of this class of converters is based upon an additive white noise model of quantization errors. Our key result is a formula that relates the minimum achievable MSE of such converters to the signal-to-noise ratio (SNR) of the scalar quantizer embedded in the feedback loop. This result allows us to obtain analytical expressions that characterize the corresponding optimal filters. We also show that, for a fixed SNR of the scalar quantizer, the end-to-end MSE of an optimal PRFQ which uses the optimal filters (which for this case turn out to be IIR) decreases exponentially with increasing oversampling ratio. Key departures from earlier work include the fact that fed back quantization noise is explicitly taken into account and that the order of the converter filters is not a priori restricted. © 2008 IEEE.
Original languageEnglish
Pages (from-to)3871-3890
Number of pages20
JournalIEEE Transactions on Signal Processing
Publication statusPublished - 1 Aug 2008
Externally publishedYes

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