14-06-2014, 02:04 PM
Power Spectral Estimation
Analysis on Bias.ppt (Size: 309 KB / Downloads: 11)
Classification & Choice
The choice between the two options is made on a balance between “simple and fast computations but inaccurate PSD estimates” Vs “computationally involved procedures but enhanced PSD estimates
Direct Methods & Limitations
Apart from the adverse effects of noise, there are two limitations in practice
Only one manifestation , known as a realisation in stochastic processes, is available
Only a finite number of terms, say , is available
Windowing
Thus an approximation is necessary. In effect we have a new signal given by
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?
Analysis
Hence it is evident that as the length of data tends to infinity the first term remains unaffected, and thus the periodogram is an inconsistent estimator of the PSD
Narrowband Signals
The spectrum to be estimated is some cases may contain narrow peaks (high Q resonances) as in speech formants or passive sonar.
The limit on resolution imposed by window length is problematic in that it causes bias.
The derived variance formulae are not accurate