Howtosignalprocessing
- What is the formula for cross-correlation?
- What is circular cross-correlation?
- How do you interpret cross-correlation results?
- How do you find the cross-correlation of two sequences?
What is the formula for cross-correlation?
Cross-correlation between Xi and Xj is defined by the ratio of covariance to root-mean variance, ρ i , j = γ i , j σ i 2 σ j 2 . γ ^ i , j = 1 N ∑ t = 1 N [ ( X i t − X ¯ i ) ( X j t − X ¯ j ) ] .
What is circular cross-correlation?
The circular cross correlation is: c(k) = sum[a(n)*conj(b(n+k))]/[norm(a)*norm(b)]; where vector b is shifted CIRCULARLY by k samples. The function doesn't check the format of input vectors a and b!
How do you interpret cross-correlation results?
If the slope is positive, the cross correlation is positive; if there is a negative slope, the cross correlation is negative. This helps to identify important lags (or leads) in the process and is useful for application when there are predictors in an ARIMA model.
How do you find the cross-correlation of two sequences?
To detect a level of correlation between two signals we use cross-correlation. It is calculated simply by multiplying and summing two-time series together. In the following example, graphs A and B are cross-correlated but graph C is not correlated to either.
