10 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…