Bartlett's method

Presented By :- Diwaker Pant112607ME (ECE)NITTTR CHD

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.

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

3

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).

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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 .

To estimate the spectral characteristics of signal characterized as random processes.

To estimation of spectra in frequency domain when signals are random in nature.

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Estimated autocorrelation:

Estimated power spectrum or periodogram:

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

Types of Nonparametric methods

Bartlett method

Welch method

Blackman-Tukey method

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.

Properties of Bartlett’s method

Bias:

Resolution:

Variance:

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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 .

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

? Querry

REFFERENCES

Salivahanan and Vallavaraj , Digital signal Processing

Emanuel C.lfeachor and Barrie W.jervis Digital Signal Processing

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