Cross-correlation

Cross correlation with FFT and fftshift

Cross correlation with FFT and fftshift
  1. What is FFT and Fftshift?
  2. What is cross-correlation in digital signal processing?
  3. What is cross-correlation in frequency domain?
  4. Why do we use Fftshift?

What is FFT and Fftshift?

fft computes the discrete Fourier transform and by definition the output is complex. fftshift doesn't compute anything except swaping the position of the samples, so if your input is real, you get real output.

What is cross-correlation in digital 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. It is commonly used for searching a long signal for a shorter, known feature.

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.

Why do we use Fftshift?

It is useful for visualizing a Fourier transform with the zero-frequency component in the middle of the spectrum. For vectors, fftshift(X) swaps the left and right halves of X . For matrices, fftshift(X) swaps quadrants one and three of X with quadrants two and four.

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