Non-Separable Linear Canonical Wavelet Transform

This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion of a non-separable linear canonical wavelet transform in L2(Rn). The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, we formulate several uncertainty inequalities, including the Heisenberg’s, logarithmic, and Nazorav’s inequalities for the proposed transform in the linear canonical domain. The obtained results are reinforced with illustrative examples.

Subclasses of Uniform Univalent Functions Associated with Srivastava and Attiya Operator

In this paper, we introduce new subclasses k−STs(p,β) and k−UKs(p,β) of analytic and univalent functions in the canonical domain associated with the Srivastava and Attiya operator. The radius problems of these subclasses regarding symmetrical points are investigated and compared with previous known results. Certain properties and conditions of these subclasses such as integral representation are also discussed in this work.

An Algorithm of DOA Estimation in Linear Canonical Transform Domain

An algorithm of DOA estimation based on linear canonical transform is proposed. In this method, the observed signals are first transformed to linear canonical domain, through selecting appropriate transformation parameters, characteristics of the observed signal appear to be energy-concentrated in the corresponding linear canonical domain, and by that, the linear canonical domain steering vector is defined, then root-MUSIC is used to estimate DOA of impinging signals. Simulation examples are provided showing the effectiveness of the presented technique.