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A new convolution theorem associated with the linear canonical transform
In this paper, we first introduce a new notion of canonical convolution
operator, and show that it satisfies the commutative, associative, and
distributive properties, which may be quite useful in signal processing.
Moreover, it is proved that the generalized convolution theorem and generalized
Young's inequality are also hold for the new canonical convolution operator
associated with the LCT. Finally, we investigate the sufficient and necessary
conditions for solving a class of convolution equations associated with the
LCT.Comment: 13 page