311 research outputs found
A Deterministic Analysis of Decimation for Sigma-Delta Quantization of Bandlimited Functions
We study Sigma-Delta () 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 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 th order 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 scheme
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
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