30-05-2012, 01:55 PM
Power Spectral Estimation
Power Spectral Estimation.ppt (Size: 314.5 KB / Downloads: 194)
The purpose of these methods is to obtain an approximate estimation of the power spectral density of a given real random process.
Classification
The crux of PSD estimation is the determination of the autocorrelation sequence from a given process.
Methods that rely on the direct use of the given finite duration signal to compute the autocorrelation to the maximum allowable length (beyond which it is assumed zero), are called Non-parametric methods
Methods that rely on a model for the signal generation are called Modern or Parametric methods.
Personally I prefer the names “Direct” and “Indirect Methods”.
The Bias
The Bias pertains to the question:
Does the estimate tend to the correct value as the number of terms taken tends to infinity?
If yes, then it is unbiased, else it is biased.
The Variance
The Variance refers to the question on the “goodness” of the estimate:
Does its variance of the estimate decrease with N? ie does the expression below tend to zero as N tends to infinity?
Smoothed Periodograms
Periodograms are therefore inadequate for precise estimation of a PSD.
To reduce variance while keeping estimation simplicity and efficiency, several modifications can be implemented
a) Averaging over a set of periodograms of (nearly) independent segments
b) Windowing applied to segments
c) Overlapping the windowed segments for additional averaging