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

Journal Article (Journal Article)

We study Sigma-Delta (Σ Δ) 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 Σ Δ 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 Σ Δ 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 Σ Δ scheme.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Saab, R

Published Date

  • November 1, 2015

Published In

Volume / Issue

  • 22 / 11

Start / End Page

  • 2093 - 2096

International Standard Serial Number (ISSN)

  • 1070-9908

Digital Object Identifier (DOI)

  • 10.1109/LSP.2015.2459758

Citation Source

  • Scopus