Non-isotropic angular Stockwell transform and the associated uncertainty principles. Issue 4 (12th March 2021)

• Record Type: Journal Article
• Authors: Shah, Firdous A.; Tantary, Azhar Y.
• Is Part Of: Applicable analysis. Volume 100:Issue 4(2021)
• Page Start: 835
• Page End: 859
• Publication Date: 2021-03-12
• Subjects: Stockwell transform -- window function -- wavelet transform -- discrete Stockwell transform -- Fourier transform -- uncertainty principle; 65R10 -- 47G10 -- 42C40 -- 42C15 -- 42A38 -- 94A12; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1622681
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: For an efficient and directional representation of signals in higher dimensions, we propose the non-isotropic angular Stockwell transform in the context of time-frequency analysis. The proposed transform is aimed at rectifying the conventional Stockwell transform by employing an angular and scalable localized window which offers directional flexibility and thereby results in the multi-scale and directional analysis of signals in higher dimensions. The basic properties of the proposed transform such as orthogonality relation, reconstruction formula, derivation of the admissibility condition and characterization of the range are discussed using the machinery of operator theory and Fourier transforms. In addition, we introduce the discrete version of the non-isotropic angular Stockwell transform and establish a sufficient condition for the corresponding discrete family to be a frame in L 2 ( R 2 ) . Furthermore, some generalizations of the well-known Heisenberg-type inequalities are derived for the non-isotropic angular Stockwell transform in the Fourier domain.