Symmetric correlation and its properties

In this paper, symmetric correlation that is a correlation between symmetrically extended signals is proposed to estimate shifts between two signals. Symmetrical extension creates smooth boundaries of endpoints of signals to avoid the discontinuity of endpoints. The symmetric correlation is performed by discrete cosine transform (DCT) without the increase of the number of samples. Moreover, it is shown that whitening of signals removes the interference effect of symmetry. That is, the correlation between signals can be directly estimated by symmetric correlation with whitening. Using the signs of DCT coefficients can be approximated as whitening, which contributes to lower computational complexity.