Wavelet transforms associated with the index Whittaker transform
Akhilesh Prasad, Jeetendrasingh Maan, Sandeep Kumar Verma
Abstract
The continuous wavelet transform (CWT) associated with the index Whittaker transform is defined and discussed using its convolution theory. Existence theorem and reconstruction formula for CWT are obtained. Moreover, composition of CWT is discussed, and its Plancherel's and Parseval's relations are also derived. Further, the discrete version of this wavelet transform and its reconstruction formula are given. Furthermore, certain properties of the discrete Whittaker wavelet transform are discussed.
Topics & Concepts
MathematicsParseval's theoremDiscrete wavelet transformContinuous wavelet transformHarmonic wavelet transformConvolution (computer science)Wavelet transformWaveletMathematical analysisStationary wavelet transformS transformConvolution theoremDiscrete Fourier transform (general)Pure mathematicsFourier transformFractional Fourier transformFourier analysisArtificial intelligenceComputer scienceArtificial neural networkMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation