14 citations · 14 across the 10 of their papers we have counts for
12 papers
Nonuniform Multiresolution Analysis Associated with Linear Canonical Transform
Firdous A. Shah, Waseem Z. Lone
The linear canonical transform (LCT) has attained respectable status within a short span and is being broadly employed across several disciplines of science and engineering includi…
Convolution Based Special Affine Wavelet Transform and Associated Multi-resolution Analysis
Firdous A. Shah, Waseem Z. Lone
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms int…
Fractional Multiresolution Analysis and Associated Scaling Functions in
Owais Ahmad, Neyaz A. Sheikh, Firdous A. Shah
In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional…
Fractional Biorthogonal wavelets in
Owais Ahmad, Neyaz A. Sheikh, Firdous A. Shah
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its application…
Special Affine Wavelet Transforms and the Corresponding Poisson Summation Formula
Firdous A. Shah, Azhar Y. Tantary, Aajaz A. Teali
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local fe…
Uncertainty Principles for the Continuous Shearlet Transforms in Arbitrary Space Dimensions
Firdous A. Shah, Azhar Y. Tantary
The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of th…
On Quaternion Shearlet Transforms
Firdous A. Shah, Azhar Y. Tantary
In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of q…
Construction of -stage Nonuniform Wavelets on Local Fields
Owais Ahmad, F. A. Shah
Shah and Abdullah [Complex Analysis Operator Theory, 9 (2015), 1589-1608] have introduced a generalized notion of nonuniform multiresolution analysis (NUMRA) on local field of…
Biorthogonal Wavelets on the Spectrum
Owais Ahmad, F. A. Shah
A generalization of Mallat's classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed (J. Funct. Anal. 158, 209-241, 19…
Inequalities for Nonuniform Wavelet Frames
Firdous A. Shah
Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set is no long…
Gabor Frames on Local Fields of Positive Characteristic
Firdous A. Shah
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and scien…
Construction of Biorthogonal Wavelet Packets on Local Fields of Positive Characteristic
F. A. Shah, M. Y. Bhat
Orthogonal wavelet packets lack symmetry which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality…