Sampling piecewise sinusoidal signals with finite rate of innovation methods

  • Authors:

  • Jesse Berent;Pier Luigi Dragotti;Thierry Blu

  • Affiliations:

  • Electrical and Electronic Engineering Department, Imperial College, London, U.K.;Electrical and Electronic Engineering Department, Imperial College, London, U.K.;Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong SAR, China

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2010

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Abstract

We consider the problem of sampling piecewise sinusoidal signals. Classical sampling theory does not enable perfect reconstruction of such signals since they are not band-limited. However, they can be characterized by a finite number of parameters, namely, the frequency, amplitude, and phase of the sinusoids and the location of the discontinuities. In this paper, we showthat under certain hypotheses on the sampling kernel, it is possible to perfectly recover the parameters that define the piecewise sinusoidal signal from its sampled version. In particular, we show that, at least theoretically, it is possible to recover piecewise sine waves with arbitrarily high frequencies and arbitrarily close switching points. Extensions of the method are also presented such as the recovery of combinations of piecewise sine waves and polynomials. Finally, we study the effect of noise and present a robust reconstruction algorithm that is stable down to SNR levels of 7 [dB].