Quantization of Bandlimited Functions Using Random Samples

Rohan Joy, Felix Krahmer, Alessandro Lupoli, Radha Ramakrishnan

Abstract: We investigate the compatibility of distributed noise-shaping quantization with random samples of bandlimited functions. Let $f$ be a real-valued $\pi$-bandlimited function. Suppose $R>1$ is a real number, and assume that $\{x_i\}_{i=1}^m$ is a sequence of i.i.d random variables uniformly distributed on $[-\tilde{R},\tilde{R}]$, where $\tilde{R}>R$ is appropriately chosen. We show that on using a distributed noise-shaping quantizer to quantize the values of $f$ at $\{x_i\}_{i=1}^m$, a function $f^{\sharp}$ can be reconstructed from these quantized values such that $\|f-f^{\sharp}\|_{L^2[-R, R]}$ decays with high probability as $m$ and $\tilde{R}$ increase.

Submission Type: Full Paper