Time Encoding Quantization of Bandlimited and Finite-Rate-of-Innovation Signals

TL;DR

This paper analyzes how quantization affects the performance of integrate-and-fire time encoding machines for bandlimited and finite-rate-of-innovation signals, providing bounds and practical insights for improved sampling accuracy.

Contribution

It derives an upper bound on the MSE of quantized IF-TEM samplers and compares it to classical ADCs, revealing conditions for superior performance.

Findings

Quantization step size can be reduced with increased signal bandwidth or pulse count.

Quantized IF-TEM can achieve roughly 8 dB lower MSE than classical ADCs with same bit count.

Experimental results confirm the theoretical MSE bounds.

Abstract

This paper studies the impact of quantization in integrate-and-fire time encoding machine (IF-TEM) sampler used for bandlimited (BL) and finite-rate-of-innovation (FRI) signals. An upper bound is derived for the mean squared error (MSE) of IF-TEM sampler and is compared against that of classical analog-to-digital converters (ADCs) with uniform sampling and quantization. The interplay between a signal's energy, bandwidth, and peak amplitude is used to identify how the MSE of IF-TEM sampler with quantization is influenced by these parameters. More precisely, the quantization step size of the IF-TEM sampler can be reduced when the maximum frequency of a bandlimited signal or the number of pulses of an FRI signal is increased. Leveraging this insight, specific parameter settings are identified for which the quantized IF-TEM sampler achieves an MSE bound that is roughly 8 dB lower than that of a classical ADC with the same number of bits. Experimental results validate the theoretical conclusions.