Correlation

Proof of Autocorrelation property of DFT

Proof of Autocorrelation property of DFT
  1. What is correlation property of DFT?
  2. How is autocorrelation calculated in DSP?
  3. What is autocorrelation and its properties?

What is correlation property of DFT?

Circular Correlation

The Complex correlation property states. Here rxy(l) is circular cross correlation which is given as. This means multiplication of DFT of one sequence and conjugate DFT of another sequence is equivalent to circular cross-correlation of these sequences in time domain.

How is autocorrelation calculated in DSP?

The autocorrelation appears in applications such as communications (matched filtering), signal modeling (normal equations), and pattern recognition (template matching). x(l − k)x(l) = rx(−k) where in the second equality we made the substitution l = n + k.

What is autocorrelation and its properties?

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them.

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