Linear Canonical Matched Filter: Theory, Design, and Applications

The linear canonical transform (LCT) is a multiparameter unitary transform that generalizes a large number of classical transforms with application to signal processing and optics. Many of its fundamental properties are already known; however, little attention has been paid to the design and implementation of matched filters in the LCT domain. The objective of this paper is to design this type of filters that maximize the output signal-to-noise ratio, dubbed the linear canonical matched filter (LCMF). We first derive some facts of the LCT spectral analysis for random signals. Then, by applying the derived results, the LCMF design theory associated with the LCT is developed. Moreover, the implementation and basic properties of the LCMF are presented. The introduction of the LCMF invites a new interpretation of the ambiguity function and the correlation function of the LCT. Finally, we provide several applications for the theoretical derivations.