Intuitive explanation of cross-correlation in frequency domain

1. What is cross-correlation in frequency domain?
2. How do you interpret cross-correlation results?
3. How do you find cross-correlation with FFT?
4. What is meant by cross-correlation?

What is cross-correlation in frequency domain?

According to the cross-correlation theorem : the cross-correlation between two signals is equal to the product of fourier transform of one signal multiplied by complex conjugate of fourier transform of another signal.

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 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 meant by cross-correlation?

Cross-correlation is used to evaluate the similarity between the spectra of two different systems, for example, a sample spectrum and a reference spectrum. This technique can be used for samples where background fluctuations exceed the spectral differences caused by changes in composition.