Power Spectral Density Estimation of Signals

We can estimate the power spectral density of signals using two primary methods: the autocorrelation function method and the periodogram approach. These techniques provide valuable insights into signal frequency characteristics and power distribution across the spectrum. The autocorrelation function method estimates the power spectrum by computing the correlation between a signal and its time-shifted version. In MATLAB implementation, this typically involves using the xcorr() function to calculate autocorrelation, followed by applying the Fourier transform via fft() to obtain the power spectral density. This method is particularly effective for stationary signals and provides better statistical properties. The periodogram method, implemented using MATLAB's periodogram() function or directly through fft() and squared magnitude calculation, estimates the power spectrum based on the signal's periodic characteristics. This approach involves computing the squared magnitude of the discrete Fourier transform of the signal segments. While computationally efficient, the periodogram may exhibit higher variance that can be mitigated using techniques like Welch's method with overlapping segments. Both methods enable us to obtain detailed and accurate power spectral density estimates, facilitating comprehensive analysis and understanding of signal properties. The choice between methods depends on factors such as signal stationarity, computational requirements, and desired spectral resolution.