Cross-correlation

The cross-correlation is a mathematical operation to compute the degree of similarity of two signals while shifting one of the signals in time. To compare e.g. repeated ultrasonic recordings in concrete, the normalized correlation coefficient (range 1 to 0 for identical to independent signals) for zero time shift is used. It can be made in both frequency domain and in the time domain. If changes are affecting the concrete, the new signal has a cross-correlation less than 1 when compared to the reference signal (before and after structural change). The correlation coefficient (or decorrelation coefficient = 1 – correlation coefficient) are calculated to quantify the waveforms changes.