Computing Power Spectral Density for Two Signals with Spectral Correlation Control

When computing the power spectral density (PSD) of two signals, we can utilize their spectral correlation coefficients to determine which frequency points should participate in superposition calculations, thereby controlling the quality of the resulting power spectral density. The spectral correlation coefficient serves as a metric to evaluate the similarity between two signals at specific frequency components, helping decide whether their respective PSD contributions should be combined. This approach can be implemented using signal processing libraries like MATLAB or Python's SciPy, where key functions such as pwelch (for PSD estimation) and cross-spectral density calculations (for correlation coefficients) would be employed. The algorithm typically involves: 1) computing individual PSDs using Welch's method, 2) calculating spectral correlation coefficients across frequency bins, 3) establishing a threshold (e.g., 0.7-0.9) for coefficient values to filter relevant frequency points, and 4) performing conditional superposition only at frequencies meeting the correlation criteria. This methodology enhances control over PSD accuracy and precision by selectively combining spectral information only where signals demonstrate significant coherence, ultimately improving the quality of computational results for applications like signal analysis and system identification.