Cross Correlation A simple yet powerful technique for detecting known patterns Example applications include Detecting preamble sequence in WiFi packets Detecting cell tower ID based on known sequences ID: 713537
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Pattern matching with Correlation and Time WarpingSlide2
Cross Correlation
A simple, yet powerful technique for detecting known patterns
Example applications include
Detecting preamble sequence in WiFi packetsDetecting cell tower ID based on known sequencesDetecting gene sequencesOther broad applications in - pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology
preamble
payload
channel is idleSlide3
Consider a sequence of complex numbers –
,
Consider its complex conjugate
,
=
Cross CorrelationSlide4
Cross Correlation
=
=
=
Phase match, the sum is high
Phase
mis
-match, the sum is low magnitudeSlide5
Cross Correlation
The phase match results in strong detection of the known pattern even in presence of noise.
For example
The sequence Z is a subsequence of another large sequence Noise has been added to itCross correlation helps detects this submerged sequence
,
Slide6
Detecting patterns
Cross-correlation can be used to detect the submerged sequence
Specifically, it answers following questions
Does the known sequence (Z) exist in the input sequenceWhere in the input sequence does Z appear?
,
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Methodology
,
Input sequence
Template sequenceSlide8
Methodology
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Methodology
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Methodology
,
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Methodology
,
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Methodology
,
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Methodology
,
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Methodology
,
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A
matlab
example
Pattern
NoiseSlide16
Pattern embedded in noise – visually not detectableSlide17
Correlation can detect the hidden patternSlide18
Correlation output when the pattern is absentSlide19
Dynamic time warpingSlide20
Consider a speech signal – “hello”Slide21
How can we detect “hello” in a large audio file
Can we use correlation?
Doesn’t work because every utterance of “hello” is not identical
For exampleSlide22
Different utterances of “hello”
Utterance - 1
Utterance - 2
They look different, some parts are elongated while others are compressed
However, overall structure looks similarSlide23
Revisit identical sequencesSlide24
Non identical but similar sequencesSlide25
Dynamic time warping (DTW)
Pattern matching technique
Similar to cross-correlation, pattern matches a known template
However, it works even when the target sequence is elongated and compressed relative to the templateSlide26
Cross-correlationSlide27
DTWSlide28
DTW
DTW is an path optimization problem
Reference -
https://link.springer.com/chapter/10.1007/978-3-540-74048-3_4Slide29
Conclusion
Correlation matches exact sequences
Applications in preamble detection, gene sequencing, cell ID detection
etcMatches sequences which are warped (elongated and compressed) relative to each otherBroad applications in cinema making, data mining, information retrieval, gesture tracking etc