Description:
The Finite Rate of Innovation (FRI) sampling theory can realize the sub-Nyquist sampling and reconstruction of the pulse streams, which aims to reconstruct the characteristic parameters rather than the time domain waveform. Different from the classical spectral estimation algorithm in this framework, we regard Discrete Cosine Transform (DCT) as the bridge between the discrete time domain and the parameter domain, and use the pure real field information to estimate the parameters in order to speed up the estimation process. Based on optimization theory, AFoD algorithm is proposed to solve the conjugate roots problem caused by DCT coefficients with which the original signal composed of K pulses per unit time can be perfectly reconstructed with only 4K samples. In order to improve the anti-noise performance of AFoD algorithm, we propose the improved MUoD and ESoD algorithms. We also design the 2DFoD algorithm for sampling and reconstruction of 2D pulses streams. Simulation results show that our estimation schemes can recover signal parameters perfectly with a low sampling rate, and the speed of parameter estimation is much faster than that of classical FRI method at the same sampling rate. The simulation experiments give the expected excellent results