Final Answer:
To calculate the normalized cross-correlation between x[k] and y[k] using x[k] as the reference sequence, you can perform extra calculations after obtaining the cross-correlation using xcorr. The formula for normalized cross-correlation (NCC) is given by NCC[m] = Cxy[m] / sqrt(Cxx * Cyy), where Cxy[m] is the cross-correlation at lag m, Cxx is the autocorrelation of x, and Cyy is the autocorrelation of y.
Step-by-step explanation:
After obtaining the cross-correlation Cxy[m] using xcorr, the next step is to calculate the autocorrelations Cxx and Cyy. Autocorrelation measures the similarity of a signal with a delayed version of itself. For Cxx, you calculate xcorr with x[k] as both input sequences. Similarly, for Cyy, you use y[k] as both input sequences. These autocorrelations are then used in the NCC formula to normalize the cross-correlation values at each lag.
The normalization ensures that the cross-correlation values are scaled appropriately, making them independent of the overall energy of the signals. This is crucial when comparing signals of different magnitudes. The final result, NCC[m], represents the degree of similarity between x[k] and y[k] at each lag m.
Values close to 1 indicate a strong positive correlation, values close to -1 indicate a strong negative correlation, and values around 0 suggest a weak or no correlation. By incorporating extra calculations for autocorrelations, the normalized cross-correlation provides a robust measure of similarity between the two signals while accounting for their individual characteristics.