Extracting Periodic Signals from Audio-Frequency Analog Strong Noise Random Signals

This article discusses methodologies for extracting periodic signals from audio-frequency analog strong noise random signals (comprising strong noise and periodic components). We will implement signal processing techniques including filtering, decomposition, and reconstruction stages. Each processing step will be thoroughly explained with corresponding MATLAB/Python code implementations, such as using FIR/IIR filters for noise reduction, employing wavelet transform for signal decomposition, and applying reconstruction algorithms to recover the target signal. Key functions like fft() for spectral analysis and xcorr() for cross-correlation calculations will be demonstrated. The computational procedures for extracting statistical parameters - including mean values, average power, variance, frequency spectrum characteristics, power spectral density, and cross-correlation metrics - will be detailed for both original and processed signals. All analytical results will be supported by comprehensive graphical representations including time-domain waveforms, frequency spectra, and correlation plots. Through experimental result analysis and discussion, we will draw conclusions regarding signal processing effectiveness and provide insights for future research directions in related fields.