Feasibility of FRI-based square-wave reconstruction with quantization error and integrator noise

Conventional Nyquist sampling and reconstruction of square waves at a finite rate will always result in aliasing because square waves are not band limited. Based on methods for signals with finite rate of innovation (FRI), generalized Analog Thresholding (gAT-n) is able to sample square waves at a much lower rate under ideal conditions. The target application is efficient, real-time, implantable neurotechnology that extracts spiking neural signals from the brain. This paper studies the effect of integrator noise and quantization error on the accuracy of reconstructed square waves. We explore realistic values for integrator noise and input signal amplitude, using specifications from the Texas Instruments IVC102 integrator chip as a first-pass example because of its readily-available data sheet. ADC resolution is varied from 1 to 16 bits. This analysis indicates that gAT-1 is robust against these hardware non-idealities where gAT-2 degrades less gracefully, which makes gAT-1 a prime target for hardware implementation in a custom integrated circuit.