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Cross-Correlation and Matched Filters

By Shehrzad Qureshi, April 01, 2003

Time-delay estimation of waveforms is of fundamental importance in signal-processing applications. Shehrzad uses matched filters, implemented via cross-correlation, to solve time delay problems.
Apr03: Algorithm Alley 


1. If x[n] or y[n] are not power-of-two lengths, make them power-of-two lengths by extending the array(s) to the appropriate length (this is called zero-padding)
2. Choose one of the inputs to time-reverse (for example, given x[l] form x[-l])
3. Apply FFT to both sequences:
   a. X[f] = FFT( x[n] )
   b. Y[f] = FFT( y[n] )
4. cross-correlation = IFFT[ (X[f])(Y[f]) ]

Example 3: Cross-correlation pseudocode. Inputs are finite sequences x[n] and y[n].



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