Math @ Duke

Publications [#287094] of Ingrid Daubechies
Papers Published
 Daubechies, I; Saab, R, A Deterministic Analysis of Decimation for SigmaDelta Quantization of Bandlimited Functions,
Ieee Signal Processing Letters, vol. 22 no. 11
(November, 2015),
pp. 20932096, Institute of Electrical and Electronics Engineers (IEEE), ISSN 10709908 [doi]
(last updated on 2019/05/26)
Abstract: © 2015 IEEE. We study SigmaDelta (Σ Δ) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then downsampling, a process known as decimation, can efficiently encode the associated Σ Δ bitstream. It allows a large reduction in the bitrate 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 bitrate. For example, this result applies to the 1bit, greedy, firstorder Σ Δ scheme.


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