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

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.

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.

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

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

Relationship between Scale and Period and its Ecological Applications in Wavelet Analysis

2013 ◽  
Vol 726-731 ◽  
pp. 4252-4257
Author(s):  
Yu Yang Song ◽  
Rong Li ◽  
Ming Yan Li ◽  
Wen Hui Zhang
Keyword(s):  
Wavelet Analysis ◽  
Distribution Pattern ◽  
Power Spectra ◽  
Wavelet Function ◽  
Haloxylon Ammodendron ◽  
Mexican Hat ◽  
Ecological Applications

The relations between the scales and periods of Mexican Hat (Mexh) and Morlet (Morl) wavelets have been deduced. Based on these relations, variances, coefficients, and power spectra of these two wavelets’ original and eco-used wavelets are compared and analyzed theoretically and experimentally for the distribution pattern of Haloxylon ammodendron Bunge population in Gurban Tonggut desert, China. The research shows that: (1) Mexh and Morl eco-used wavelets can be simultaneously used to describe the distribution period of Haloxylon population and to study the same phenomenon by combining these two wavelet advantages. (2) The primary period value identified using Mexh eco-used wavelet than using its original wavelet is closer to the true one, while Morl eco-used wavelet helps find all changes in the period earlier. (3) For the same wavelet function, with its period enlarging, its primary period can be found in a smaller scale, inversely found later.

scholarly journals The De-Noising of Sonic Echo Test Data through Wavelet Transform Reconstruction

1999 ◽  
Vol 6 (5-6) ◽  
pp. 267-272 ◽  
Author(s):  
J.N. Watson ◽  
P.S. Addison ◽  
A. Sibbald
Keyword(s):  
Wavelet Transform ◽  
Test Data ◽  
Discrete Wavelet ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Transform Method ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Non Destructive

This paper presents the results of feasibility study into the application of the wavelet transform signal processing method to sonic based non-destructive testing techniques. Finite element generated data from cast in situ foundation piles were collated and processed using both continuous and discrete wavelet transform techniques. Results were compared with conventional Fourier based methods. The discrete Daubechies wavelets and the continuous Mexican hat wavelet were used and their relative merits investigated. It was found that both the continuous Mexican hat and discrete Daubechies D8 wavelets were significantly better at locating the pile toe compared than the Fourier filtered case. The wavelet transform method was then applied to field test data and found to be successful in facilitating the detection of the pile toe.

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