scholarly journals A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Felipe A. Apolonio ◽  
Daniel H. T. Franco ◽  
Fábio N. Fagundes
Keyword(s):  
Wavelet Transform ◽  
Phase Space ◽  
High Frequency ◽  
Continuous Wavelet ◽  
Boundary Values ◽  
Tempered Distribution ◽  
Proper Convex ◽  
Directional Wavelets ◽  
Directional Wavelet ◽  
Finite Sum

By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in thek-space of frequencies), in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of the wavelet transform. Moreover, we show that for a given distributionf∈𝒮′(ℝn), the continuous wavelet transform offwith respect to a conical wavelet is defined in such a way that the directional wavelet transform offyields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set off.

scholarly journals Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n )

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 235 ◽  
Author(s):  
Jagdish Pandey ◽  
Jay Maurya ◽  
Santosh Upadhyay ◽  
Hari Srivastava
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Weak Topology ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
Tempered Distributions ◽  
Tempered Distribution ◽  
Wavelet Inversion ◽  
Constant Distribution

In this paper, we define a continuous wavelet transform of a Schwartz tempered distribution f ∈ S ′ ( R n ) with wavelet kernel ψ ∈ S ( R n ) and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of S ′ ( R n ) . It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Analogue CMOS high-frequency continuous wavelet transform circuit

1999 ◽  
Vol 35 (1) ◽  
pp. 4 ◽  
Author(s):  
E.W. Justh ◽  
F.J. Kub
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Continuous Wavelet

Development of Spike Wavelet Analysis and Its Application to Damage Analysis on Gearbox

2006 ◽  
Vol 321-323 ◽  
pp. 1233-1236
Author(s):  
Sang Kwon Lee ◽  
Jang Sun Sim
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Low Frequency ◽  
Gear System ◽  
Frequency Resolution ◽  
Linear Scaling ◽  
Continuous Wavelet ◽  
Vibration Signals ◽  
Gear Fault

Impulsive sound and vibration signals in gear system are often associated with their faults. Thus these impulsive sound and vibration signals can be used as indicators in condition monitoring of gear system. The traditional continuous wavelet transform has been used for detection of impulsive signals. However, it is often difficult for the continuous wavelet transform to identify spikes at high frequency and meshing frequencies at low frequency simultaneously since the continuous wavelet transform is to apply the linear scaling (a-dilation) to the mother wavelet. In this paper, the spike wavelet transform is developed to extract these impulsive sound and vibration signals. Since the spike wavelet transform is to apply the non-linear scaling, it has better time resolution at high frequency and frequency resolution at low frequency than that of the continuous wavelet transform respectively. The spike wavelet transform can be, therefore, used to detect fault position clearly without the loss of information for the damage of a gear system. The spike wavelet transform is successfully is applied to detection of the gear fault with tip breakage.

scholarly journals Analysis of the High-Frequency Content in Human QRS Complexes by the Continuous Wavelet Transform: An Automatized Analysis for the Prediction of Sudden Cardiac Death

Sensors ◽  
2018 ◽  
Vol 18 (2) ◽  
pp. 560 ◽  
Author(s):  
Daniel García Iglesias ◽  
Nieves Roqueñi Gutiérrez ◽  
Francisco De Cos ◽  
David Calvo
Keyword(s):  
Wavelet Transform ◽  
Sudden Cardiac Death ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Cardiac Death ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
High Frequency Content

scholarly journals Continuous Wavelet Transform of Schwartz Tempered Distributions in $S'(\mathbb R^n)$

2019 ◽  
Author(s):  
Jagdish Narayan Pandey ◽  
Jay Singh Maurya ◽  
Santosh Kumar Upadhyay ◽  
Hari Mohan Srivastava
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Weak Topology ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
Tempered Distributions ◽  
Tempered Distribution ◽  
Wavelet Inversion ◽  
Constant Distribution

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

scholarly journals The continuous wavelet transform in processing data of high frequency electromagnetic prospecting

2016 ◽  
Vol 19 (2) ◽  
pp. 81-93
Author(s):  
Tin Quoc Chanh Duong ◽  
Dau Hieu Duong ◽  
Van Thanh Nguyen ◽  
Thuan Van Nguyen
Keyword(s):  
Wavelet Transform ◽  
Data Processing ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Theoretical Models ◽  
Vital Role ◽  
Continuous Wavelet ◽  
Ground Penetrating ◽  
Non Destructive ◽  
Shallow Structure

Ground Penetrating Radar (GPR), a high frequency electromagnetic prospecting method (10 to 3000 MHz) has been rapidly developed in recent decades. With many advantages such as non-destructive, fast data collection, high precision and resolution, this method is a useful means to detect underground targets. It is currently used in the research of studying the shallow structure for examples: forecast landslide, subsidence, mapping urban underground works, traffic, construction, archaeology and other various fields of engineering, GPR data processing is becoming increasingly urgent. Wavelet transform is one of the new signal analysis tools, plays a vital role in numerous domains like image processing, graphics, data compression, gravitational, electromagnetic and geomagnetic data processing, GPR and some others. In this study, we used the continuous wavelet transform (CWT) and multiscale edge detection (MED) with the wavelet functions which were appropriately selected to determine underground targets. The accuracy of this technique was tested on some theoretical models before being applied on experimental data. The obtained results showed that this was a feasible method that could be used to detect the size and position of the anomaly objects.

A Search Method for Unknown High-Frequency Oscillators in Noisy Signals Based on the Continuous Wavelet Transform

2019 ◽  
Vol 80 (7) ◽  
pp. 1279-1287
Author(s):  
I. V. Shcherban ◽  
N. E. Kirilenko ◽  
S. O. Krasnikov
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
High Frequency ◽  
Search Method ◽  
Continuous Wavelet ◽  
Noisy Signals
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