Year: 2019
Type: article
Abstract: We consider the problem of recovering a continuoustime bandlimited signal from the discrete-time signal, obtained from sampling it every Tsseconds and reducing the result modulo Δ, for some Δ > 0. For Δ = ∞, the celebrated Shannon-Nyquist sampling theorem guarantees that perfect recovery is possible, provided that the sampling rate 1/Tsexceeds the so-called Nyquist rate. Recent work by Bhandari et al. has shown that for any Δ > 0 perfect reconstruction is still possible, if the sampling rate exceeds the Nyquist rate by a factor of ire. In this letter, we improve upon this result and show that for finite energy signals, perfect recovery is possible for any Δ > 0 and any sampling rate above the Nyquist rate. Thus, modulo folding does not degrade the signal, provided that the sampling rate exceeds the Nyquist rate. This claim is proved by establishing a connection between the recovery problem of a discrete-time signal from its modulo reduced version and the problem of predicting the next sample of a discrete-time signal from its past, and leveraging the fact that for a bandlimited signal the prediction error can be made arbitrarily small.
Source: IEEE Signal Processing Letters
Authors: Elad Romanov, Or Ordentlich
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2930502000