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We study Sigma-Delta ( &#x03A3;&#x0394;) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated &#x03A3;&#x0394; bit-stream. It allows a large reduction in the bit-rate while still permitting good approximation of the underlying bandlimited function via an appropriate reconstruction kernel. Specifically, in the case of stable rth order &#x03A3;&#x0394; schemes we show that the reconstruction error decays exponentially in the bit-rate. For example, this result applies to the 1-bit, greedy, first-order &#x03A3;&#x0394; scheme.

A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions