Innovation rate sampling of non-ideal piecewise polynomials

Recent sampling results show that ideal piecewise polynomials can be modelled as finite-rate-of-innovation (FRI) signals and perfectly recovered by spectral estimation. However, there is no any generic FRI model for non-ideal piecewise polynomials. An FRI model is proposed as an extension of the VPW-FRI (pulses with variable width) model for non-ideal piecewise polynomials which have uncertain transition zones near discontinuity points. The derivative of non-ideal piecewise polynomials as differentiated VPW pulse streams is assumed. The proposed model can be sampled by arbitrary kernels and recovered by a modified annihilating filter. For the extended model, simulation results analyse several factors that affect the model anti-noise property and verify its superiority of better matching performance for real non-ideal signals in comparison of the FRI model for ideal piecewise polynomials.