Finite-precision effects on graph filters
Luiz F. O. Chamon, Alejandro Ribeiro · 2017
Graph filters play a fundamental role in graph signal processing. In practice, however, the finite precision nature of digital computers introduces numerical errors that can hinder their performance and jeopardize their usefulness. To mitigate these effects, this work investigates the numerical behavior of graph filters in finite-precision arithmetic. It derives a closed-form expression for the variance of the quantization noise at the filter output and shows how the filter coefficients interact with the spectrum of the shift operator to affect the numerical performance of graph filters. Based on these results, the paper then provides an optimally weighted shrinkage regularizer that can be used to design filters robust to quantization errors. Bit-accurate experiments illustrate the performance of different designs and show the importance of considering numerical effects when designing graph filters.