✦ LIBER ✦
Coarse quantization of highly redundant time–frequency representations of square-integrable functions
✍ Scribed by Özgür Yılmaz
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 411 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1063-5203
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✦ Synopsis
We introduce a family of coarse quantization algorithms for heavily oversampled Gabor expansions of certain classes of functions in L 2 (R). These algorithms, which we call the TF quantization algorithms, are inspired by sigma-delta modulation, a widely implemented coarse quantization scheme for oversampled bandlimited functions. We show that the TF algorithms produce weak type approximations where modulation spaces M 1,1 m with suitable weight functions m are the appropriate test function spaces. We also show that the TF algorithms are translation invariant up to some uniform correction.