The wave packet transform in the framework of linear canonical transform

2021 ◽  
Author(s):  
Akhilesh Prasad ◽  
Z. A. Ansari
Keyword(s):  
Wave Packet ◽  
Inversion Formula ◽  
Wavelet Function ◽  
Linear Canonical Transform ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.

Applications of Mexican Hat Wavelet Function to Binary Mixture Analysis

2009 ◽  
Vol 59 (12) ◽  
Author(s):  
Ozgur Ustundag ◽  
Erdal Dinc ◽  
Dumitru Baleanu
Keyword(s):  
Wavelet Function ◽  
Mixture Analysis ◽  
Zero Crossing ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Relative Standard ◽  
Sensitivity And Selectivity ◽  
Crossing Point ◽  
Zero Points

The simultaneous determination of pyridoxine hydrochloride (B6) and isoniazide (INH) in tablets was performed by using the Mexican hat wavelet function (MEXH). The absorption spectra of B6, INH and their samples were recorded in the spectral range of 200-330 nm. Linear regression functions for B6 and INH in the linear concentration range of 5-45 mg/mL were obtained by measuring the transformed signals at 253.5 nm corresponding to the zero-crossing point for INH and at 270.6 nm corresponding to the zero-points for B6, respectively. The validation of MEXH method was performed by using the synthetic mixtures. The percent mean recoveries and their relative standard deviations were found as 98.7% and 2.06 for B6 and 98.9 % and 1.89 for INH in the synthetic mixture analysis. The MEXH method was applied to the real samples and a good sensitivity and selectivity was reported. The MEXH method was sucessfully compared with classical derivative method.

scholarly journals The circuit realization of Mexican Hat wavelet function

2005 ◽  
Vol 59 (6) ◽  
pp. 370-373 ◽  
Author(s):  
Nalan Özkurt ◽  
F. Acar Savacı ◽  
Mustafa Gündüzalp
Keyword(s):  
Wavelet Function ◽  
Circuit Realization ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Abelian theorems for fractional wavelet transform

2017 ◽  
Vol 10 (01) ◽  
pp. 1750019
Author(s):  
Akhilesh Prasad ◽  
Praveen Kumar
Keyword(s):  
Wavelet Transform ◽  
Wavelet Function ◽  
Tempered Distributions ◽  
Final Value ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Fractional Wavelet Transform ◽  
Abelian Theorems

In this paper, initial and final value Abelian theorems for fractional wavelet transform of function and tempered distributions are obtained. Using Mexican hat wavelet function, an application for Abelian theorems is investigated.

THE BACK-PROJECTION METHOD FOR CONSTRUCTING 3D NON-TENSOR PRODUCT MOTHER WAVELETS AND THE APPLICATION IN IMAGE EDGE DETECTION

2012 ◽  
Vol 10 (03) ◽  
pp. 1250026 ◽  
Author(s):  
LI ZENG ◽  
JIQIANG GUO ◽  
CHENCHENG HUANG
Keyword(s):  
Tensor Product ◽  
Computational Cost ◽  
Three Dimension ◽  
Back Projection ◽  
Mother Wavelet ◽  
3D Images ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Directional Wavelets ◽  
Mother Wavelets

In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.

Three-Dimensional Profilometry Based on Mexican Hat Wavelet Transform

2009 ◽  
Vol 29 (1) ◽  
pp. 197-202 ◽  
Author(s):  
周翔 Zhou Xiang ◽  
赵宏 Zhao Hong
Keyword(s):  
Wavelet Transform ◽  
Three Dimensional ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

Product of continuous fractional wave packet transforms

2019 ◽  
Vol 17 (04) ◽  
pp. 1950021
Author(s):  
Akhilesh Prasad ◽  
Praveen Kumar ◽  
Tanuj Kumar
Keyword(s):  
Fourier Transform ◽  
Wave Packet ◽  
Inversion Formula ◽  
Fractional Fourier Transform

In this paper, we investigated the fractional Fourier transform (FrFT) of the continuous fractional wave packet transform and studied some properties of continuous fractional wave packet transform. The product of continuous fractional wave packet transforms (CFrWPTs) is defined. Parseval’s relation and an inversion formula for product of CFrWPT are obtained. An example is also given.

Foreground Separation Methods for Satellite and Balloon Experiments

2005 ◽  
Vol 201 ◽  
pp. 71-74
Author(s):  
R. Belén Barreiro ◽  
Michael P. Hobson ◽  
Anthony N. Lasenby ◽  
Patricio Vielva ◽  
Enrique Martínez-González ◽  
...  
Keyword(s):  
Point Source ◽  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Balloon Experiments ◽  
Combined Technique ◽  
Physical Components ◽  
Planck Satellite

A combined technique using the maximum-entropy method (MEM) and the mexican hat wavelet (MHW) to separate and reconstruct the physical components of the microwave sky is presented. We apply this method to simulated observations by the ESA Planck satellite in small patches of the sky. The reconstructed maps of the CMB and foregrounds are improved as compared to those obtained with MEM on its own. Moreover, more accurate point source catalogues are produced at each observing frequency. This technique may also be extended to deal with other multifrequency CMB experiments, including all-sky data.

scholarly journals Combining maximum-entropy and the Mexican hat wavelet to reconstruct the microwave sky

2001 ◽  
Vol 328 (1) ◽  
pp. 1-16 ◽  
Author(s):  
P. Vielva ◽  
R.B. Barreiro ◽  
M.P. Hobson ◽  
E. Martínez-González ◽  
A.N. Lasenby ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Mexican Hat Wavelet ◽  
Mexican Hat

The wave packet transform associated with the linear canonical transform

Optik ◽  
2015 ◽  
Vol 126 (21) ◽  
pp. 3168-3172
Author(s):  
Yuan-Min Li ◽  
Deyun Wei
Keyword(s):  
Wave Packet ◽  
Linear Canonical Transform
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