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WAVELET-BASED RECONSTRUCTION FOR UNLIMITED SAMPLING

Rudresh, Sunil and Adiga, Aniruddha and Shenoy, Basty Ajay and Seelamantula, Chandra Sekhar (2018) WAVELET-BASED RECONSTRUCTION FOR UNLIMITED SAMPLING. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), APR 15-20, 2018, Calgary, CANADA, pp. 4584-4588.

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Abstract

Self-reset analog-to-digital converters (ADCs) allow for digitization of a signal with a high dynamic range. The reset action is equivalent to a modulo operation performed on the signal. We consider the problem of recovering the original signal from the measured modulo-operated signal. In our formulation, we assume that the underlying signal is Lipschitz continuous. The modulo-operated signal can be expressed as the sum of the original signal and a piecewise-constant signal that captures the transitions. The reconstruction requires estimating the piecewise-constant signal. We rely on local smoothness of the modulo-operated signal and employ wavelets with sufficient vanishing moments to suppress the polynomial component. We employ Daubechies wavelets, which are most compact for a given number of vanishing moments. The wavelet filtering provides a sequence consisting of a sum of scaled and shifted versions of a kernel derived from the wavelet filter. The transition locations are estimated from the sequence using a sparse recovery technique. We derive a sufficient condition on the sampling frequency for ensuring perfect reconstruction of the smooth signal. We validate our reconstruction technique on a signal consisting of sinusoids in both clean and noisy conditions and compare the reconstruction quality with the recently developed repeated finite-difference method.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belong to IEEE
Keywords: Wavelets; unlimited sampling; self-reset ADC; vanishing moments; sparse recovery
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 25 Oct 2018 14:31
Last Modified: 25 Oct 2018 14:31
URI: http://eprints.iisc.ac.in/id/eprint/60958

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