Generating Sequences with Fixed Autocorrelation Coefficients in MATLAB

This MATLAB implementation generates sequences with specified autocorrelation coefficients and visualizes their power spectral density. Using autoregressive (AR) models or the Yule-Walker equations, the code constructs sequences matching predefined correlation structures. The analysis extends to examining spectral characteristics including peak frequencies and spectral shapes through MATLAB's signal processing toolbox functions like pwelch() or periodogram(). Understanding these frequency-domain properties enables deeper insights into signal behavior for applications spanning signal processing, communications systems, and control engineering.

For implementation, the ar_model() function can generate sequences with target autocorrelation, while spectral analysis utilizes Welch's method for robust PSD estimation. The workflow involves parameterizing correlation coefficients, generating corresponding sequences, and comparing theoretical versus computed spectral densities to validate the approach.