Crosscorrelation

The concept of autocorrelation and spectra is easily generalized to crosscorrelation and cross-spectra.

Consider two Z-transforms X(Z) and Y(Z). The cross-spectrum C(Z) is defined by  

$$C(Z) \eq \overline{X} \left( \frac{1}{Z} \right) \ Y(Z)$$ (48)

The crosscorrelation function is the coefficients c_k. If some particular coefficient c_k in C(Z) is greater than any of the others, then it is said that the waveform x_t most resembles the waveform y_t if either x_t or y_t is delayed k time units with respect to the other.