Power Spectrum Estimation Methods (Periodogram, Welch, and PMUSIC)

Power spectrum estimation is a fundamental signal processing technique used to analyze the frequency characteristics of signals. Common methods include the Periodogram, Welch's method, and PMUSIC algorithm. The Periodogram method estimates the power spectrum by decomposing the signal into periodic components and calculating the power spectrum of each component, typically implemented using Fast Fourier Transform (FFT) operations with proper windowing functions. Welch's method improves spectral estimation by dividing the signal into overlapping segments, computing periodograms for each segment, and averaging them to reduce variance - this approach can be implemented using functions like pwelch in MATLAB with configurable segment length and overlap parameters. PMUSIC (Pisarenko Harmonic Decomposition) is a maximum likelihood-based estimation technique that optimizes model parameters through eigen-decomposition of the signal's covariance matrix, often implemented using algorithms like pmusic in signal processing toolboxes. These methods play crucial roles in signal processing applications, enabling analysis and research of various signal types including biomedical signals, communication signals, and vibration analysis.