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

: Boche, H.; Mönich, U.J.

Mathar, R. ; Informationstechnische Gesellschaft -ITG-:
8th International ITG Conference on Source and Channel Coding, SCC 2010. CD-ROM : Dedicated to the memory of Ralf Kötter, January, 18 - 21, 2010 in Siegen, Germany
Berlin: VDE-Verlag, 2010 (ITG-Fachbericht 219)
ISBN: 978-3-8007-3211-1
6 pp.
International Conference on Source and Channel Coding (SCC) <8, 2010, Siegen>
Conference Paper
Fraunhofer HHI ()

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.