Research ArticleNo Access

Novel special affine wavelet transform and associated uncertainty principles

Owais Ahmad

https://orcid.org/0000-0002-9903-2656

Department of Mathematics, National Institute of Technology, Srinagar-190006, Jammu and Kashmir, India

E-mail Address: siawoahmad@gmail.com

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and

Neyaz A. Sheikh

Department of Mathematics, National Institute of Technology, Srinagar-190006, Jammu and Kashmir, India

E-mail Address: neyaznit@yahoo.co.in

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https://doi.org/10.1142/S0219887821500559Cited by:12 (Source: Crossref)

Abstract

Due to the extra degrees of freedom, special affine Fourier transform (SAFT) has achieved a respectable status within a short span and got versatile applicability in the areas of signal processing, image processing, sampling theory, quantum mechanics. However, due to its global kernel, SAFT fails to obtain local information of non-transient signals. To overcome this, in this paper, we introduce the concept of novel special affine wavelet transform (NSAWT) and extend key harmonic analysis results to NSAWT analogous to those for the wavelet transform. We first establish some fundamental properties including Moyal’s principle, Inversion formula and the range theorem. Some Heisenberg type inequalities and Pitt’s inequality are established for SAFT and consequently Heisenberg uncertainty principle is derived for NSAWT.

Keywords:

AMSC: 42C40, 42B10, 65R10, 42C15

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