Sampling Finite Rate of Innovation Signals with Chebyshev Polynomials

Finite Rate of Innovation (FRI) sampling has been widely used to sampling parametric signals at sub-Nyquist sampling rates. Nevertheless, real-world systems generally handle real-valued signals, posing challenges for acquiring complex domain Fourier coefficients directly. To overcome this limitation, we propose a Chebyshev polynomial-based FRI sampling framework that enables processing entirely in the real domain. Projecting the FRI signal onto the Chebyshev basis and employing a improved annihilating filter reformulates the parameter estimation problem into a classical spectral estimation task. Furthermore, the integration of the discrete Hilbert transform allows for a further reduction in both sampling channels and total sample count. Numerical simulations validate the effectiveness of the proposed approach and the generalizability of FRI theory across different signal bases.