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Autocorrelation and Crosscorrelation Analysis

The document discusses autocorrelation and crosscorrelation of signals. It provides examples of calculating the autocorrelation of signal x(n)=0.9n and the crosscorrelation of x(n) and y(n)=0.8-n. It also discusses using crosscorrelation to estimate the delay between an original audio signal x(n) and its echoes y(n)=x(n)+αx(n-k). The conclusion summarizes that autocorrelation yields a symmetric result while crosscorrelation does not, and that correlation compares similarities between signals while convolution manipulates signals.

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J Arnold Samson
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265 views5 pages

Autocorrelation and Crosscorrelation Analysis

The document discusses autocorrelation and crosscorrelation of signals. It provides examples of calculating the autocorrelation of signal x(n)=0.9n and the crosscorrelation of x(n) and y(n)=0.8-n. It also discusses using crosscorrelation to estimate the delay between an original audio signal x(n) and its echoes y(n)=x(n)+αx(n-k). The conclusion summarizes that autocorrelation yields a symmetric result while crosscorrelation does not, and that correlation compares similarities between signals while convolution manipulates signals.

Uploaded by

J Arnold Samson
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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SAMSON JOHN ARNOLD L.

T41 – SIGPROL

Machine Problem

1. Using the cov_m function, determine the autocorrelation sequence rxx(l) and the
crosscorrelation sequence rxy(l) for the following sequences.

x(n) = 0.9n , 0 ≤ n ≤ 20 ;

y(n) = 0.8-n , -20 ≤ n ≤ 0

Describe your observation of these results


OUTPUT:

 The Auto correlation of the signal as displayed is symmetrical. This is further proven with the
symmetrical property of correlation. The coding principle and steps were almost the same
when compared to that of the convolution except that the second signal is flipped.
 The plot for Cross correlation is not symmetrical. This type of correlation is used to
determine the degree of difference and similarities between two or more signals.

2. In a certain concert hall, echoes of the original audio signal x(n) are generated due to the
reflections at the walls and ceiling. The audio signal experienced by the listener y(n) is a
combination of x(n) and its echoes. Let

y(n) = x(n) + αx(n-k)

where k is the amount of delay in samples and α is its relative strength. We want to estimate the
delay using correlation analysis.
1. Determine analytically the crosscorrelation ryx(l) in terms of the autocorrelation rxx(l).
2. Let x(n) = cos(0.2πn) + 0.5cos(0.6 πn), α = 0.1, and k = 50. Generate 200
samples of y(n) and determine its correlation. Can you obtain α and k by observing ryx(l)?
CONCLUSION:

As a whole generalization, correlation is the process of

comparing the differences and similarities present

between two or more signals. Convolution is the process

of manipulating signals. It may be altered or improved

mathematically. Dissimilar in computing for the signal’s

convolution, the correlation does not need to be

flipped. It may be worked upon directly. The signal is

no longer shifted. The degree of similarity between

signals is the primary purpose for correlating signals.

Modifying, altering and performing signal manipulation

falls under convolution. Cross correlation does not

evidently yield a symmetric output signal. Only when

performing Auto correlation does it results in a

symmetric signal response.

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