03-05-2013, 03:59 PM
Welch Estimation
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SPECTRAL DENSITY ESTIMATION
Estimating power spectral density of a WSS process is called spectrum estimation
The spectral density characterizes the frequency content of the signal.
The purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.
Spectral estimation has great importance in many Applications including data analysis, wiener filtering , signal Detection, classification, and tracking, etc.
WELCH ESTIMATION
Welch proposed two modifications to Bartlett’s method:
Allow the data segments to overlap;
2 Apply a data window w to each sequence thereby producing a set of modified periodograms to be averaged
The data segments can be represented as ,
xi(n)= xi(n+iD) n=0,1,…,M-1 i=0,1,…,L-1
where iD is the starting point of the i th sequence.
If D=M the segment do not overlap
If D=M/2,50% overlap between successive data segments.