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Define and Explain:

i. Auto correlation:

ii. Cross correlation:

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 05

Year : MAY 2014

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(i) Auto correlation:

When we calculate correlation function of the signal with itself, then it is called Autocorrelation$(R_{xx} ).$

Auto correlation is a method which is frequently used for the extraction of fundamental frequency, if a copy of the signal is shifted in phase, the distance between correlation peaks is taken to be the fundamental period of the signal.

The method may be combined with the simple smoothing operations of peak and centre clipping or with other LPF.

Autocorrelation$(R_{xx} (t))$ for continuous time signal is given by $(R_{xx} (t))= ∫\limits_{-∞}^∞ x(k)x(k-t)dk.$

Autocorrelation$(R_{xx} (n))$ for discrete time signal is given by $(R_{xx} (n)) = ∑\limits_{k=-∞}^∞ x(k)x(k-n).$

(ii) Cross correlation:

When we calculate correlation function of two different signals, then it is called Cross-correlation $(R_{xh} ).$

Cross-correlation is the method which basically underlies implementations of the Fourier transform, signals of varying frequency and phase are correlated with the input signals and the degree of correlation in terms of frequency and phase represents the frequency and phase spectrums of input signal.

Cross-correlation $(R_{xh} (t))$ for continuous time signal is given by $(R_{xh} (t)) = ∫\limits_{-∞}^∞ x(k)h(k-t)dk.$

Cross-correlation$(R_{xh} (n))$ for discrete time signal is given by $(R_{xh} (n)) = ∑\limits_{k=-∞}^∞x(k)h(k-n).$

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Auto Correlation Cross Correlation
Autocorrelation is also known as serial correlation it is the cross-correlation of a signal with itself. Cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them.
It is the similarity between observations as a function of the time lag between them. It is a function of a time-lag applied to one of waveform.
A plot of auto correlation coefficient vs lag is called correlogram. Cross-correlation coefficient can be plotted against lag to produce cross-correlogram
To calculate coefficient deduction of auto-correlation coefficient is used Calculation of coefficient is same like that of deduction of auto-correlation coefficient.