bartlett's method pp ts
DESCRIPTION
digital signal processingTRANSCRIPT
April 12, 2023Presented by Diwaker Pant
The signal processing methods which characterises the frequency content of signal is known as spectrum analysis.
We know that the signals which are analysed in any communication system are either purely random or will have noise component also.
If the signal is random ,then only an estimate of the signal can be obtained.
This is possible only if the statistical attributes of the random signals are known.
April 12, 2023Presented by Diwaker Pant
The signal energy is given by Parseval’s relation-:
The density of the energy of x(t) w.r.t. frequency is represented by |X(f)|2
where |X(f)|2 = Sxx(f)
Where Sxx(f) = Energy spectral density
April 12, 2023Presented by Diwaker Pant
Let Rxx(Ʈ) be the autocorrelation function of the signal x(t) where Rxx(Ʈ) is given by
Rxx(Ʈ) =
The Fourier transform of autocorrelation function is given by Sxx(f)
Where Sxx(f) is power spectral density of signal x(t).
April 12, 2023Presented by Diwaker Pant
Autocorrelation function of a random process is statistical average that will use to characterizing random signal in the time domain .
Fourier transform of that autocorrelation function is called power density spectrum.
Power Spectral Estimation method is to obtain an approximate estimation of the power spectral density of a given real random process .
April 12, 2023Presented by Diwaker Pant
To estimate the spectral characteristics of signal characterized as random processes.
To estimation of spectra in frequency domain when signals are random in nature.
April 12, 2023Presented by Diwaker Pant
kN
nx nxknx
Nkr
1
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)(*)(1
)(ˆ
k
jkx
jkper ekreP )(ˆ)(ˆ
Estimated autocorrelation:
Estimated power spectrum or periodogram:
April 12, 2023 Presented by Diwaker Pant
Non-parametric PSE does NOT assume any data-generating process or model i.e no assumption about how data were generated.
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
April 12, 2023 Presented by Diwaker Pant
Types of Nonparametric methods
Bartlett method
Welch method
Blackman-Tukey method
April 12, 2023 Presented by Diwaker Pant
Bartlett’s method for reducing the variance in the periodogram involves three steps .
The N-point sequence is subdivided into K nonoverlapping segments where each segment has length L .This results in K data segments.
For each segment, Compute the periodogram .
Averaging the periodogram for the K segment to obtain the Bartlett power spectrum estimate.
April 12, 2023 Presented by Diwaker Pant
Properties of Bartlett’s method
Bias:
Resolution:
Variance:
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kePVar
April 12, 2023Presented by Diwaker Pant
The effect of reducing the length of data from N point to L=N/K , results in a window whose spectral width has been increased by factor K. Consequently ,the frequency resolution has been reduced by factor K.
Reduction in the resolution have reduced the variance .
April 12, 2023Presented by Diwaker Pant
Measurement of noise spectra for the design of optimal linear filter
Feature Extraction
In biomedical , seismology
For Meteorological data , Communication Engg.
In industrial process control
April 12, 2023Presented by Diwaker Pant
? Querry
April 12, 2023 Presented by Diwaker Pant
REFFERENCES
Salivahanan and Vallavaraj , Digital signal Processing
Emanuel C.lfeachor and Barrie W.jervis Digital Signal Processing
www.google.com www.wikipedia.com
April 12, 2023 Presented by Diwaker Pant
April 12, 2023 Presented by Diwaker Pant