Relationship between time average and cross spectrum

1. What is cross correlation in signal processing?
2. What is the cross correlation function corresponding to the cross power density spectrum?
3. How do you find cross correlation with FFT?
4. What is cross spectrum analysis?

What is cross correlation in signal processing?

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.

What is the cross correlation function corresponding to the cross power density spectrum?

Cross-correlation function is a function that defines the relationship between two random signals. The cross power spectral density, S_xy❲f❳is complex-valued with real and imaginary parts given by co spectrum ❲Co_xy❲f❳❳and quadrature spectrum ❲Qu_xy❲f❳❳respectively.

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 spectrum analysis?

Cross spectral analysis allows one to determine the relationship between two time series as a function of frequency.