Innovation rate sampling of non‐ideal piecewise polynomials
Ning Fu, Guoxing Huang, Liwen Sun, Liyan Qiao · Electronics Letters · 2018
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.