Cross-correlation

Mismatched offset when computing cross-correlation using FFT

Mismatched offset when computing cross-correlation using FFT
  1. How do you find cross-correlation with FFT?
  2. How do you calculate cross-correlation?
  3. Is cross-correlation commutative?
  4. How does cross-correlation work?

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.

How do you calculate cross-correlation?

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.

Is cross-correlation commutative?

Cross correlation is not commutative like convolution i.e. If R12(0) = 0 means, if ∫∞−∞x1(t)x∗2(t)dt=0, then the two signals are said to be orthogonal.

How does cross-correlation work?

Cross-correlation is a measurement that tracks the movements of two or more sets of time series data relative to one another. It is used to compare multiple time series and objectively determine how well they match up with each other and, in particular, at what point the best match occurs.

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