Performance analysis and optimal filter design for sigma-delta modulation via duality with DPCM

Or Ordentlich, Uri Erez
<span title="">2015</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="" style="color: black;">2015 IEEE International Symposium on Information Theory (ISIT)</a> </i> &nbsp;
Sampling above the Nyquist-rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (minimum mean-squarederror) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a low-pass filter at the decoder. The goal of this work is to characterize the optimal trade-off between the per-sample quantization rate and the resulting mean-squared-error distortion, under various
more &raquo; ... ons on the feedback filter. To this end, we establish a duality relation between the performance of sigma-delta modulation, and that of differential pulse-code modulation when applied to (discrete-time) band-limited inputs. As the optimal trade-off for the latter scheme is fully understood, the full characterization for sigma-delta modulation, as well as the optimal feedback filters, immediately follow.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1109/isit.2015.7282469</a> <a target="_blank" rel="external noopener" href="">dblp:conf/isit/OrdentlichE15</a> <a target="_blank" rel="external noopener" href="">fatcat:syzdvk5ntveidpvgd7noyjpz4a</a> </span>
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