Power Spectrum Analysis

Application Background

Power spectrum, abbreviated from power spectral density function, defines signal power per unit frequency band. It characterizes how signal power varies with frequency, illustrating the distribution of signal power in the frequency domain. In MATLAB implementation, this can be computed using functions like pwelch() or periodogram() with proper windowing techniques to reduce spectral leakage.

Key Technologies

The power spectral density definition offers a power characterization approach different from time-domain methods, widely applied in statistical signal processing. Two primary applications include:

(1) Definition of white noise and colored noise.

If a signal's power spectrum remains constant across frequencies (Sxx(f) = constant), the random process is classified as white noise. Otherwise, it's considered colored noise. Programmatically, this can be verified using isequal() function to check spectrum uniformity after computing power spectral density through FFT-based methods.

(2) By leveraging the relationship between power spectral density and autocovariance function, the signal's autocorrelation function can be derived. Specifically, the autocorrelation function can be obtained through inverse Fourier transform of the power spectrum, implemented using ifft() function in computational analysis.

Therefore, power spectral density serves as a crucial tool for analyzing signal characteristics in frequency domain and identifying noise types, with practical implementation involving signal processing toolboxes for accurate spectral estimation.