Multi-Channel FRI Sampling System Based on Non-Ideal Filters

We mainly focus on the sampling issues in relation to the pulse streams whose shapes have been recognized. The recent finite rate of innovation (FRI) framework can sample impulsive streams at rates much lower than the Nyquist rate, but the non-ideal effect of physical components was not considered during the practices in previous works. In this paper, we propose a multi-channel FRI sampling method based on non-ideal filter. By using appropriately selected cosine signals to modulate the input signal in each channel, the input signal's dominant frequency band is shifted to baseband and then filtered by a non-ideal Low-Pass Filters (LPF), we can obtain a distributed multi-set of Fourier coefficients. Since the non-ideal effect of the filter will reduce the recovery ability of the system, we propose an effective method to eliminate the influence of the non-ideal effect of the filter combined with the multi-channel sampling structure. By using sparsity based recovery algorithm, the pulse streams are recovered from the obtained samples with high precision. In addition, we completed the design and implementation of the hardware prototype, which reduced the complexity of the hardware system and improved the flexibility of the sampling system. Finally, results from simulations and hardware tests show that our strategy improves noise robustness.