Double linear correlation using DCT and its application to forward and reverse matching

We propose a method of double linear correlation, which enables simultaneous calculation of the linear correlation between a sequence and a template and of the linear correlation between the sequence and the reversed template. Using the symmetric property of the discrete cosine transform (DCT) basis, we need to neither expand sequences symmetrically nor reverse the template. Proper zero-padding in the spatial domain before and after the sequences is considered to isolate the two linear correlations. The proposed method requires DCT types 1 and 2. The computational complexity of the proposed method is lower than that using fast Fourier transform.