The linear canonical transform plays an important role in engineering and many
applied fields, as it is the case of optics and signal processing. In this paper, a new
convolution for the linear canonical transform is proposed and a corresponding product
theorem is deduced. It is also proved a generalized Young's inequality for the introduced
convolution operator. Moreover, necessary and sufficient conditions are obtained for the
solvability of a class of convolution type integral equations associated with the linear
canonical transform. Finally, the obtained results are implemented in multiplicative
filters design, through the product in both the linear canonical transform domain and
the time domain, where specific computations and comparisons are exposed.Fundação para a Ciência e Tecnologiapublishe
