Summary

This blog explains practical techniques to synthesize two or more signals that exhibit a specified cross-correlation or N×N covariance matrix. It walks through mathematical approaches (e.g., Cholesky and eigen decompositions) and implementation considerations for generating correlated multichannel random processes useful for simulation and testing.

Key Takeaways

• Construct a target covariance matrix that encodes desired variances and cross-correlations between channels.
• Apply Cholesky or eigen (Karhunen–Loève) decompositions to transform white noise into correlated Gaussian signals.
• Implement spectral shaping to impose frequency-domain cross-spectral properties when stationarity or colored spectra are required.
• Validate results by estimating sample covariance and power spectral densities and comparing them to the specified targets.

Who Should Read This

Intermediate DSP engineers and researchers who need to simulate correlated multichannel signals for testing algorithms in communications, radar, or audio systems.

TimelessIntermediate

Topics