Separation of overlapping non-stationary signals and compressive sensing-based reconstruction using instantaneous frequency estimation

Compressive sensing uses an incomplete sample set to consider signal reconstruction with sparse basis representations over a specific transform domain. This work examines the difficulties encountered in various signal processing applications, such as data overlap with the target signal in time and frequency domains. The conventional filtering and windowing processes fail to promote better results in recovering the desired signal. The non-stationary signal with time-frequency representations is highly significant for certain valuable applications. An efficient signal separation and reconstruction method based on instantaneous frequency estimate is proposed to improve the non-stationary signal outcome. The proposed research includes speech signal data acquisition, signal component decomposition, instantaneous frequency estimation, overlapped signal separation, and reconstruction. Two datasets, Dacon Overlapped Speech and LJ Speech Dataset, are utilized to generate a new overlapped signal dataset. Initially, the generated speech signals are collected and decomposed into several monocomponents using Synchrosqueezing Wavelet Transform (SynWav), Renyi's quadratic entropy (RQuad), Narrow bandpass filtering (NBand) and single frequency filtering (SFreq). The instantaneous frequencies are estimated using the Hilbert-Huang transform (HilHuT) to generate a time-frequency representation of multicomponent signals. The overlapped signals are separated and reconstructed to a desired signal using a Compressive sensing-based Discrete Cosine transform with amended intrinsic chirp separation (CDcT_AIChirS). The proposed model is simulated using PYTHON to examine the performances. In comparison, the mean square error is calculated to be 2.71, the root mean square error is calculated to be 1.64, and the signal to noise ratio is calculated to be 32dB.