On the impact of thresholding and quantization on the behavior of bandlimited systems and signals

In this paper we analyze the impact of thresholding and quantization on the approximation of bandlimited signals and systems by sampling series that only use samples of the signal taken at the Nyquist rate. We show that there are stable systems that become unstable if the samples are quantized. For these systems the approximation error is unbounded irrespective of how small the quantization step size is chosen. Furthermore, we completely characterize the systems for which the approximation is stable under thresholding and quantization. Surprisingly, this class of systems is the well-known class of bounded-input bounded-output (BIBO) stable systems. Moreover, we discuss the special case of finite impulse response (FIR) filters and give an upper bound for the approximation error that shows the dependence of the error on the filter length.