02-01-2013, 12:44 PM
DIGITAL SIGNAL PROCESSING
[attachment=46133]
THEORY
CROSS CORRELATION:
It is a measure of similarity of two wave
forms as a function of a time-lag applied to
one of them. This is also known as sliding dot
product or inner-product. It is commonly
used to search a long duration signal for a
shorter, known feature. It also has application
in pattern recognition,single particle analysis, electron topographic averaging, cryptanalysis and neurophysiology.
For discrete functions, the cross-correlation is
Defined as:
The cross-correlation is similar in nature to the convolution of two functions.whereas convolution involves reversing a signal, then shifting it and multiplying by another signal, correlation only involves shifting it and multiplying(no reversing).
AUTO CORRELATION:
It is the cross-correlation of a signal wit itself. Informally,it is the similarity between observations as a function of the time seperation between them.It is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal which has been buried under noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.
CONCLUSION
FROM ABOVE EXPERIMENT WE HAVE STUDIED THE AUTO-CORRELATION AND CROSS-CORRELATION OF TWO SEQUENCE.
[attachment=46133]
THEORY
CROSS CORRELATION:
It is a measure of similarity of two wave
forms as a function of a time-lag applied to
one of them. This is also known as sliding dot
product or inner-product. It is commonly
used to search a long duration signal for a
shorter, known feature. It also has application
in pattern recognition,single particle analysis, electron topographic averaging, cryptanalysis and neurophysiology.
For discrete functions, the cross-correlation is
Defined as:
The cross-correlation is similar in nature to the convolution of two functions.whereas convolution involves reversing a signal, then shifting it and multiplying by another signal, correlation only involves shifting it and multiplying(no reversing).
AUTO CORRELATION:
It is the cross-correlation of a signal wit itself. Informally,it is the similarity between observations as a function of the time seperation between them.It is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal which has been buried under noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.
CONCLUSION
FROM ABOVE EXPERIMENT WE HAVE STUDIED THE AUTO-CORRELATION AND CROSS-CORRELATION OF TWO SEQUENCE.