Lecture 18:EE 221: Signals Analysis and Systems

Instructor: Dr. Ghazi Al SukkarDept. of Electrical EngineeringThe University of JordanEmail: ghazi.alsukkar@ju.edu.jo

Correlation functions: Correlation refers to the degree by which things are related.

Correlation functions define the similarity between two signals .

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For energy signals: The cross correlation between x(t) and y(t)

Some use :

For real-valued signals :

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Use this

Cont.. Relative between Correlation and Convolution (for real

signals):

Hence,

But we know that for real-valued signals:

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Cont.. Autocorrelation : correlation of a signal with itself.

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Cont.. For real-valued signals :

i.e., is an even function.

Fourier Transform of and ESD:

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Cont..

Or

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For power signals: The cross correlation between and :

For real-valued signals:

For periodic signals:

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Cont.. Autocorrelation functions:

For real-valued signals:

For periodic signals:

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Cont.. Also

Relation between Autocorrelation function and PSD:

Proof:

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Cont..

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