Convolution and correlation theorems associated with the octonion linear canonical transform

In this paper, a new convolution operator associated with octonion-valued signal is defined. Then a novel convolution theorem for the octonion linear canonical transform (OCLCT) is obtained. We discuss a fast algorithm of the convolution theorem related to the OCLCT. Moreover, according to a new correlation operator of the octonion-valued signal, a correlation theorem of the OCLCT is given. Finally, we obtain a product theorem of the OCLCT.