A computing method for linear convolution in the DCT domain

We propose a computing method for linear convolution between sequences using discrete cosine transform (DCT). Zero padding is considered as well as linear convolution using discrete Fourier transform (DFT). Analyzing the output range of the resulting convolution, we derive the minimum number of zero-padding before and after the sequences. The proposed method requires DCT-2 and DCT-1 transforms regardless of sequences, and can calculate linear convolution with both linear phase filter and non-linear phase filter. The computational complexity of the proposed method is lower than that of linear convolution using DFT. In addition, the proposed method can be used for computation of linear correlation between two sequences.