autospectrum
Autospectrum, or auto-spectral density, is a concept in signal processing that describes how the power of a signal or random process is distributed across frequency. For a real-valued, second-order stationary process X(t), the autocorrelation function is R_xx(τ) = E[X(t) X(t+τ)]. The autospectrum S_xx(f) is the Fourier transform of R_xx(τ). By the Wiener-Khinchin theorem, S_xx(f) and R_xx(τ) contain the same information about the signal's structure, with S_xx(f) representing the expected power at frequency f.
In discrete-time form, with r_xx[m] = E[x[n] x[n+m]], the autospectrum is given by S_xx(ω) = sum over m
Estimating the autospectrum from finite data typically involves computing a periodogram, and often using averaging techniques
Applications of autospectrum analysis span engineering and science, including communications, vibration analysis, acoustics, geophysics, and biomedical