The process of determining the spectrum of a signal based on the actual measurements
is called spectrum estimation. Power Spectral Density (PSD) describes how the power
of a signal is distributed with frequency. The PSD quantifies the signal strength in the
frequency domain.The goal of spectral density estimation is:To estimate the spectral density of a random signal from a sequence of time
samples of the signal.To describe the distribution of power contained in a signal, based on a finite
set of data.
The various methods of spectrum estimation available are: Nonparametric methods, Parametric methods, Subspace methods.
Parametric methods can yield higher resolutions than nonparametric methods in cases
where the signal length is short. These methods use a different approach for spectral
estimation instead of trying to estimate the PSD directly from the data, they model
the data as the output of a linear system driven by white noise, and then attempt
to estimate the parameters of that linear system.
The Yule-Walker AR method of spectral estimation computes the AR parameters by
forming a biased estimate of the signal’s autocorrelation function, and solving the
least squares minimization of the forward prediction error. In detail, in this method
we first assume the system parameters which satisfy the conditions of a stable
system, and we compute the output of the system for a given input.
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