Extraction, Detection, and Analysis of Weak Signals with MATLAB Implementation

This article discusses the extraction, detection, and analysis of weak signals. The following MATLAB implementation steps can be employed to complete this process: 1. Preliminary signal analysis: Compute fundamental statistical metrics including mean (using mean()), mean square value (mean(x.^2)), variance (var()), frequency spectrum (via fft()), and power spectral density (using pwelch() or periodogram()) to verify the presence of useful signal components within the input signal. 2. Signal extraction and characterization: After applying signal extraction techniques (such as filtering with filter() or wavelet denoising with wdenoise()), calculate the extracted signal's statistical parameters (mean, mean square value, variance) and probability density (through histcounts() or ksdensity()). Additionally, perform spectral analysis to obtain frequency spectrum and power spectral density. 3. Visualization: Generate comprehensive plots using MATLAB's plotting functions (plot(), stem(), or pspectrum()) to visualize the extracted signal's characteristics, enabling better interpretation of signal properties. Through this structured approach, we can systematically analyze and understand the characteristics of weak signals while extracting valuable information through quantitative and graphical representations.