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Autocorrelation & Cross-Correlation Applications: "Pattern Recognition" "Signal Detection."

Cross-correlation and autocorrelation are used for pattern recognition and signal detection. Autocorrelation is used to extract radar signals to improve sensitivity by detecting periodic radar pulse trains. Cross-correlation is used to establish symbol timing by comparing an incoming signal to a known bit sequence. Correlation is also used to analyze fractal patterns and for applications like measuring fast signal decay, laser microscopy, and musical beat estimation.

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Dhanaa Dhanagopal
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253 views4 pages

Autocorrelation & Cross-Correlation Applications: "Pattern Recognition" "Signal Detection."

Cross-correlation and autocorrelation are used for pattern recognition and signal detection. Autocorrelation is used to extract radar signals to improve sensitivity by detecting periodic radar pulse trains. Cross-correlation is used to establish symbol timing by comparing an incoming signal to a known bit sequence. Correlation is also used to analyze fractal patterns and for applications like measuring fast signal decay, laser microscopy, and musical beat estimation.

Uploaded by

Dhanaa Dhanagopal
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 PDF, TXT or read online on Scribd
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Autocorrelation & Cross-correlation Applications

Cross-correlation and autocorrelation are commonly used for


measuring the similarity of signals especially for pattern
recognition and for signal detection.

Example: Autocorrelation used to extract radar signals to


improve sensitivity. Makes use of radar signals being periodic
so the signal is a pulse train (parameters: amplitude, pulse
width and interval between pulses).

Example: Cross-correlation used to establish symbol timing by


comparing an incoming signal with a known bit sequence to
identify a known bit pattern to reference to for system timing.

Example: Correlation is used for analyzing fractal patterns.

Cross-corrrelation & Autocorrelation 1


Example: Autocorrelation Application

Autocorrelation
measurements have
become a standard
method for pulse
characterization of
ultrafast laser pulses.

Cross-corrrelation & Autocorrelation 2


General Categories of Applications
Cross-correlation and autocorrelation used for

Measuring fast signal decay


Laser microscopy
Measuring pulse broadening and distortion
Fluorescence spectroscopy
measuring musical beats (estimating pitch)
Scanning pulsar frequencies
Analyzing spatial patterns
Used in X-ray diffraction data analysis
Security system design (pattern recognition utilized)
Water traffic monitoring
and many others . . . .

Cross-corrrelation & Autocorrelation 3


Some General Relationships in Correlation

The autocorrelation function of a power signal g(t ) is given by


T /2
1
T T
Rgg ( ) lim g(t ) g(t )dt
T /2

The autocorrelation function Rgg ( ) and power spectral density


are a Fourier transform pair,
Rgg ( ) Sgg ( f )
The average power Pave is
Pave Rgg (0)
The power spectral density (PSD) transfers across a network as
2
Syy ( f ) H ( f ) Sgg ( f )

Cross-corrrelation & Autocorrelation 4

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