8th International Conference on
Computational Harmonic Analysis

September 12-16, 2022

Ingolstadt, Germany

"Quantization techniques for concentrated signals in the space of bandlimited functions"

Joy, Rohan

A key problem in signal processing is to obtain a digital representation of a function in a signal space suitable for storage, transmission and recovery. This goal is usually attained through two steps, sampling and quantization. In sampling, we sample the function at appropriate data points such that the function can be stably reconstructed using those samples. In the second step of quantization, we reduce these real or complex valued function samples to a discrete finite set known as the quantization alphabet. Sampling schemes such as uniform sampling, non-uniform sampling and random sampling, among others, have been studied for bandlimited functions and other signal spaces like shift-invariant spaces and reproducing kernel Hilbert spaces. Our work studies and explores quantization techniques in these spaces while imposing the required conditions when working with infinite-dimensional spaces. We work with different quantization techniques and compare their relative performances.

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