Generation and Analysis of a Narrowband Random Process with Computational Methods

This documentation presents a MATLAB-based workflow for generating a narrowband random process meeting specified conditions. The implementation involves developing subroutines to calculate key statistical properties including the mean function (using time-averaging techniques), autocorrelation function (computed via time-domain correlation or FFT-based methods), power spectral density (derived through periodogram or Welch's method), and signal characteristics such as the envelope (extracted via Hilbert transform), squared envelope, and instantaneous phase. The computational approach employs MATLAB's signal processing toolbox functions like hilbert() for analytic signal generation, xcorr() for correlation analysis, and pwelch() for spectral estimation. Finally, we visualize the results through one-dimensional probability density plots using histogram functions and kernel density estimation techniques, providing comprehensive analytical insights into the narrowband random process's statistical behavior.