Adapted Decimation on Finite Frames for Arbitrary Orders of Sigma-Delta Quantization

In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the Σ Δ quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate....

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2020-02, Vol.26 (1), Article 20
Main Author: Lin, Kung-Ching
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analog to digital conversion
Approximations and Expansions
Data storage
Decay rate
Fourier Analysis
Information storage and retrieval
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Measurement
Oversampling
Partial Differential Equations
Polynomials
Reconstruction
Signal,Image and Speech Processing
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Summary:In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the Σ Δ quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. We build on our previous result, which extended signal decimation to finite frames, albeit only up to the second order. In this study, we introduce a new scheme called adapted decimation, which yields polynomial reconstruction error decay rate of arbitrary order with respect to the oversampling ratio, and exponential with respect to the bit-rate.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-020-09728-8