Cross corelation between two complex-valued Time Series Objects

1. What is cross-correlation in time series?
2. How do you find the cross-correlation of two sequences?
3. How do you find cross-correlation with FFT?
4. What is cross-correlation coefficient?

What is cross-correlation in time series?

Cross correlation presents a technique for comparing two time series and finding objectively how they match up with each other, and in particular where the best match occurs. It can also reveal any periodicities in the data.

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.

How do you find cross-correlation with FFT?

We can compute correlations using the FFT as follows: FFT the two data sets, multiply one resulting transform by the complex conjugate of the other, and inverse transform the product. The result (call it rk) will formally be a complex vector of length N.

What is cross-correlation coefficient?

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature.