Power Spectral Density Estimation

The periodogram is the raw FFT magnitude squared of a signal window, and has very high variance for random signals. Welch's method divides the signal into overlapping segments, computes periodograms of each segment, and averages them. This averaging dramatically reduces variance at the cost of lower frequency resolution. For practical use, Welch's method is almost always preferred over raw periodogram.

Longer windows provide better frequency resolution but higher variance; shorter windows reduce variance but worsen frequency resolution. A practical rule is to use window length such that you have at least 8-16 overlapping segments from your data. For example, with 10 seconds of data at 1000 Hz sampling (10,000 samples), use window lengths of 512-1024 samples. Experiment and visualize to find the best balance for your application.

Parametric methods like Yule-Walker AR estimation can provide high frequency resolution with limited data. Use them when you have short signals or need very fine frequency resolution and can justify fitting an autoregressive model. However, they require choosing model order correctly and can produce spurious peaks if order is wrong. For most applications, Welch's method is more robust; use parametric methods only when their advantages outweigh added complexity.

PSD magnitude indicates average power at each frequency. Peaks in the PSD represent dominant frequency components. Use log scale for PSD (dB) to visualize components across wide dynamic range. However, distinguish between real signal components and spectral leakage artifacts by examining the shape—leakage from strong components spreads power across nearby frequencies. Use appropriate window functions and sufficient frequency resolution to minimize leakage.