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In this paper, we propose a reconstruction approach for a multiple-sinusoidal signal. The signal reconstruction requires a small number of samples and is based on a sub-Nyquist sampling scheme with dual rate channels. In the proposed sampling scheme, the samples are grouped into multiple cosets. To obtain enough different cosets to reconstruct a signal, the sampling rates of channels are required to be relative coprime. For each coset, the Whittaker–Shannon interpolation formula is employed to construct the relation between the sub-Nyquist samples and the original signal, which is used to construct the measurement matrix. Since the multiple-sinusoidal signal is sparse in the frequency domain, compressed sensing theory can be adopted to reconstruct the signal. Simulation results are reported to demonstrate the feasibility and effectiveness of the proposed approach.

The time-interleaved analog-to-digital converters (TIADCs) technique is an efficient solution to improve the sampling rate of the acquisition system with low-speed ADCs. However, channel mismatches such as gain mismatch, time skew mismatch, and offset mismatch may seriously degrade the performance of TIADC. Furthermore, for high-speed signal acquisition, the gain and time skew mismatches would vary with the signal frequency, and the traditional fixed model does not work any longer. In this paper, a series of sinusoidal signals are adopted to estimate the variable mismatches. First, an autocorrelation-based approach is presented to estimate the gain mismatch. The information about the gain mismatch is extracted from the autocorrelation function of sub-ADC output samples. Then, the time skew mismatch is estimated by utilizing the particle swarm optimization algorithm. The reported simulation results show that the mismatches can be accurately estimated. Finally, a commercial 12.5 GSPS four-channel TIADC system is utilized to verify the performance of the proposed method. The spurious free dynamic range of the system can be improved by about 20 dB, and the effectiveness of the proposed estimation method is demonstrated.

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