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.
Liu et al. (Thu,) studied this question.