Reconstructing signal from quantized signal based on singular spectral analysis

Abstract

Singular spectral analysis (SSA) is a nonparametric spectral estimation method for performing the time series analysis. It represents a signal as the sum of its components. In this manuscript, a nearly cyclostationary signal is considered. The signal is quantized and the SSA is employed to reconstruct the original signal based on the quantized signal. First, the reconstructed signal is modeled as the weighted sum of the SSA components. In order to estimate the weights, each quantization level is considered as a class. Different signal values are associated with different probabilities of the corresponding classes via the sigmoid functions defined based on the distances between the signal values and the corresponding quantized levels. Therefore, our proposed method provides the optimal estimate of a given signal in the minimum cross entropy sense. Computer numerical simulation results show that our proposed method can reduce the quantization error and reconstruct the original signal more accurately compared to some existing algorithms.