Wavelet transforms associated with the Kontorovich–Lebedev transform

2017 ◽  
Vol 15 (02) ◽  
pp. 1750011 ◽  
Author(s):  
Akhilesh Prasad ◽  
U. K. Mandal
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Discrete Version ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Basic Properties

The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich–Lebedev transform (KL-transform) and discuss some of its basic properties. Plancherel’s as well as Parseval’s relation and Reconstruction formula for CWT are obtained and some examples are also given. The discrete version of the wavelet transform associated with KL-transform is also given and reconstruction formula is derived.

Continuous wavelet transform associated with zero-order Mehler–Fock transform and its composition

2018 ◽  
Vol 16 (06) ◽  
pp. 1850050 ◽  
Author(s):  
Akhilesh Prasad ◽  
S. K. Verma
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Convolution Operator ◽  
Zero Order ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Basic Properties ◽  
Time Invariant

The continuous wavelet transform (CWT) associated with zero-order Mehler–Fock transform (MF-transform) is defined and discussed its some basic properties, Plancherel’s and Parseval’s relations, reconstruction formula for CWT are obtained. Further composition of CWT is investigated and then its Parseval’s and Plancherel’s relations are given. Moreover, time-invariant filter has been defined and proved convolution operator and wavelet transform are represented as time-invariant transform.

scholarly journals Inversion of Weinstein intertwining operator and its dual using Weinstein wavelets

2016 ◽  
Vol 24 (1) ◽  
pp. 289-307
Author(s):  
Abdessalem Gasmi ◽  
Hassen Ben Mohamed ◽  
Néji Bettaibi
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Continuous Wavelet Transforms ◽  
Intertwining Operator

Abstract In this paper, we consider the Weinstein intertwining operator ℜa, dW and its dual tR a,dW. Using these operators, we give relations between the Weinstein and the classical continuous wavelet transforms. Finally, using the Weinstein continuous wavelet transform, we deduce the formulas which give the inverse operators of R a,dW and tR a,dW.

scholarly journals Quantitative feature analysis of continuous analytic wavelet transforms of electrocardiography and electromyography

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170250 ◽  
Author(s):  
Mark P. Wachowiak ◽  
Renata Wachowiak-Smolíková ◽  
Michel J. Johnson ◽  
Dean C. Hay ◽  
Kevin E. Power ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Theme Issue ◽  
Practical Applications ◽  
Time Frequency ◽  
New Family ◽  
Physiological Processes ◽  
Analytic Wavelet

Theoretical and practical advances in time–frequency analysis, in general, and the continuous wavelet transform (CWT), in particular, have increased over the last two decades. Although the Morlet wavelet has been the default choice for wavelet analysis, a new family of analytic wavelets, known as generalized Morse wavelets, which subsume several other analytic wavelet families, have been increasingly employed due to their time and frequency localization benefits and their utility in isolating and extracting quantifiable features in the time–frequency domain. The current paper describes two practical applications of analysing the features obtained from the generalized Morse CWT: (i) electromyography, for isolating important features in muscle bursts during skating, and (ii) electrocardiography, for assessing heart rate variability, which is represented as the ridge of the main transform frequency band. These features are subsequently quantified to facilitate exploration of the underlying physiological processes from which the signals were generated. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

COMPLEMENTARY ANALYSIS TO HEART SOUNDS WHILE USING THE SHORT TIME FOURIER AND THE CONTINUOUS WAVELET TRANSFORMS

2007 ◽  
Vol 19 (05) ◽  
pp. 331-339
Author(s):  
S. M. Debbal ◽  
F. Bereksi-Reguig
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Continuous Wavelet Transforms ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Short Time

This paper presents the analysis and comparisons of the short time Fourier transform (STFT) and the continuous wavelet transform techniques (CWT) to the four sounds analysis (S1, S2, S3 and S4). It is found that the spectrogram short-time Fourier transform (STFT), cannot perfectly detect the internals components of these sounds that the continuous wavelet transform. However, the short time Fourier transform can provide correctly the extent of time and frequency of these four sounds. Thus, the STFT and the CWT techniques provide more features and characteristics of the sounds that will hemp physicians to obtain qualitative and quantitative measurements of the time-frequency characteristics.

scholarly journals Moment asymptotic expansions of the wavelet transforms

2017 ◽  
Vol 35 (1) ◽  
pp. 237
Author(s):  
Ashish Pathak
Keyword(s):  
Wavelet Transform ◽  
Asymptotic Expansions ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
Distribution Theory ◽  
Continuous Wavelet ◽  
The Moment ◽  
Distribution Spaces

Using distribution theory we present the moment asymptotic ex-pansion of continuous wavelet transform in dierent distribution spaces for largeand small values of dilation parameter a. We also obtain asymptotic expansionsfor certain wavelet transform.

The wavelet transform on spaces of type S

2006 ◽  
Vol 136 (4) ◽  
pp. 837-850 ◽  
Author(s):  
R. S. Pathak ◽  
S. K. Singh
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Wavelet Transforms ◽  
The Other ◽  
Continuous Wavelet ◽  
Continuous Linear ◽  
Ultradifferentiable Functions ◽  
Linear Map ◽  
The One

The continuous wavelet transform is studied on certain Gel'fand–Shilov spaces of type S. It is shown that, for wavelets belonging to the one type of S-space defined on R, the wavelet transform is a continuous linear map of the other type of the S-space into a space of the same type (latter type) defined on R × R+. The wavelet transforms of certain ultradifferentiable functions are also investigated.

scholarly journals Continuous wavelet transform on local fields

2015 ◽  
Vol 34 (2) ◽  
pp. 113-121 ◽  
Author(s):  
Ashish Pathak
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Local Fields ◽  
Continuous Wavelet ◽  
Mother Wavelet ◽  
Basic Properties

The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution are also studied.

An Continuous Wavelet Transform-Based Detection Approach to Traffic Anomalies

2011 ◽  
Vol 130-134 ◽  
pp. 2098-2102
Author(s):  
Ding De Jiang ◽  
Cheng Yao ◽  
Zheng Zheng Xu ◽  
Peng Zhang ◽  
Zhen Yuan ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Network Traffic ◽  
Wavelet Transforms ◽  
Detection Threshold ◽  
Continuous Wavelet ◽  
Continuous Wavelet Transforms ◽  
Traffic Characteristics ◽  
Analysis Theory ◽  
Detection Approach

Anomalous traffic often has a significant impact on network activities and lead to the severe damage to our networks because they usually are involved with network faults and network attacks. How to detect effectively network traffic anomalies is a challenge for network operators and researchers. This paper proposes a novel method for detecting traffic anomalies in a network, based on continuous wavelet transform. Firstly, continuous wavelet transforms are performed for network traffic in several scales. We then use multi-scale analysis theory to extract traffic characteristics. And these characteristics in different scales are further analyzed and an appropriate detection threshold can be obtained. Consequently, we can make the exact anomaly detection. Simulation results show that our approach is effective and feasible.

scholarly journals On alternative wavelet reconstruction formula: a case study of approximate wavelets

2014 ◽  
Vol 1 (2) ◽  
pp. 140124 ◽  
Author(s):  
Elena A. Lebedeva ◽  
Eugene B. Postnikov
Keyword(s):  
Wavelet Transform ◽  
Wide Class ◽  
Continuous Wavelet Transform ◽  
Morlet Wavelet ◽  
Continuous Wavelet ◽  
Reconstruction Formula ◽  
Physical Processes ◽  
Admissibility Condition ◽  
Oscillatory Dynamics

The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.

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