Effect of Random Sampling on Noisy Nonsparse Signals in Time-Frequency Analysis
Résumé
The paper examines the exact error of randomly sampled reconstructed nonsparse signals having a sparsity constraint. When signal is randomly sampled, it looses the property of sparsity. It is considered that the signal is reconstructed as sparse in the joint time-frequency domain. Under this assumption, the signal can be reconstructed by a reduced set of measurements. It is shown that the error can be calculated from the unavailable samples and assumed sparsity. Unavailable samples degrade the sparsity constraint. The error is examined on nonstationary signals, with the short-time Fourier transform acting as a representative domain of signal sparsity. The presented theory is verified on numerical examples