A Quantum Wavelet Uncertainty Principle

2021 ◽  
Vol 6 (1) ◽  
pp. 8
Author(s):  
Sabrine Arfaoui ◽  
Maryam G. Alshehri ◽  
Anouar Ben Ben Mabrouk
Keyword(s):  
Wavelet Transform ◽  
Uncertainty Principle ◽  
Wavelet Function ◽  
Bessel Operator ◽  
Two Parameters

In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some q-quantum wavelet, is established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is used for exploring a wavelet uncertainty principle in the q-calculus framework.

Wavelet transform on regression trend curve and its application in financial data

2020 ◽  
Vol 18 (05) ◽  
pp. 2050040 ◽  
Author(s):  
Xiaohui Zhou
Keyword(s):  
Wavelet Transform ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Financial Data ◽  
Discrete Wavelet ◽  
Reconstruction Algorithms ◽  
Regression Curve ◽  
Growth Trend ◽  
Wavelet Filters ◽  
New Research

In this paper, wavelet transform on a regression curve is investigated by using length-preserving projection and its application in financial data is also discussed. First, properties of wavelet filters on the regression trend curves are studied and two-scale equation of wavelet function is deduced on the regression trend curves. Second, the decomposition and reconstruction algorithm of discrete wavelet transform on regression trend curves is derived. Finally, two examples in financial data are given for discussion, based on decomposition and reconstruction algorithms on regression trend curves. Some new research interpretations are presented in dealing with financial data such as “volatility on regression growth trend”, “error on regression growth trend”, and so on.

An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform

2019 ◽  
Vol 17 (05) ◽  
pp. 1950030
Author(s):  
Hua Yi ◽  
Peichang Ouyang ◽  
Tao Yu ◽  
Tao Zhang
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Discrete Fourier Transform ◽  
Time Domain ◽  
Morlet Wavelet ◽  
Wavelet Function ◽  
Linear Convolution ◽  
Calculation Results ◽  
Morlet Wavelet Transform ◽  
The Time Domain

Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work.

On-Line Seam Detection in Rolling Processes Using Snake Projection and Discrete Wavelet Transform

2007 ◽  
Vol 129 (5) ◽  
pp. 926-933 ◽  
Author(s):  
Jing Li ◽  
Jianjun Shi ◽  
Tzyy-Shuh Chang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Projection Method ◽  
Discrete Wavelet ◽  
On Line ◽  
Feature Preserving ◽  
Two Parameters ◽  
T2 Control Chart ◽  
Speed And Accuracy ◽  
Selection Of

This paper describes the development of an on-line quality inspection algorithm for detecting the surface defect “seam” generated in rolling processes. A feature-preserving “snake-projection” method is proposed for dimension reduction by converting the suspicious seam-containing images to one-dimensional sequences. Discrete wavelet transform is then performed on the sequences for feature extraction. Finally, a T2 control chart is established based on the extracted features to distinguish real seams from false positives. The snake-projection method has two parameters that impact the effectiveness of the algorithm. Thus, selection of the parameters is discussed. Implementation of the proposed algorithm shows that it satisfies the speed and accuracy requirements for on-line seam detection.

scholarly journals Penentuan Notasi Gamelan Rindik Menggunakan Metode Transformasi Wavelet

2018 ◽  
Vol 17 (3) ◽  
pp. 319
Author(s):  
I Gusti Made Meri Utama Yasa ◽  
Linawati Linawati ◽  
N Paramaita
Keyword(s):  
Neural Network ◽  
Feature Extraction ◽  
Wavelet Transform ◽  
Probabilistic Neural Network ◽  
Wavelet Function ◽  
Discrete Wavelet ◽  
Daubechies Wavelet ◽  
Data Process ◽  
Average Accuracy ◽  
Accuracy Level

Abstract—This paper present about recognition of gamelan rindik pattern using wavelet transform. Wavelet transform is used to find the special characteristic of gamelan rindik, which had previously been recorded and stored in computer with format *.wav. The data was subsequently used as training and tested data, Probabilistic Neural Network (PNN) was used to recognize gamelan rindik pattern using. The training and tasted data process used four different rindics, consisting 0f 240 gamelan rindik data. Discrete Wavelet Transform (DWT) was used as the method of feature extraction, with Symlet, Haar, and Daubechies Wavelet function. Those three functions of the wavelet  shows the average accuracy level for Symlet 94.58%, Haar 93.33%, and wavelet Daubechies 94.58%.

scholarly journals Processing the Cardio Signals of Wavelet Function

2020 ◽  
Vol 9 (4) ◽  
pp. 2151-`2153
Keyword(s):  
Wavelet Transform ◽  
Wavelet Function ◽  
Binary Codes ◽  
Vector Representation ◽  
Ecg Signals ◽  
Delta Functions

A method for processing and analyzing ECG signals based on wavelet transform in an electrocardiography system is proposed. The ECG spectrum is arranged in a series of Gaussian delta functions. A method of vector representation of data in binary codes is proposed. This method allows you to detect minor changes in subsequent studies.

The efficiency of using wavelet transforms for filtering noise in the signals of measuring transducers

2021 ◽  
pp. 16-21
Author(s):  
Yuriy K. Taranenko
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Threshold Value ◽  
Wavelet Function ◽  
Threshold Function ◽  
Discrete Wavelet ◽  
Threshold Method ◽  
Wavelet Filtering ◽  
Vanishing Moments ◽  
Measuring Signal

Methods of wavelet filtering of noise in signals of measuring transducers using the threshold method of discrete wavelet transform are considered. To study the methods of wavelet filtering of noise, special model signals were used to estimate the filtering errors. A method has been developed for determining the parameters of wavelet filtering of noise with a threshold for all levels of decomposition, which makes it possible to determine the wavelet function, threshold function and filtering threshold of the detailing coefficients of the discrete wavelet decomposition. The influence of the parameters of the noise distribution, the noise level, the number of vanishing moments of the Daubechies wavelet function, the nature of the threshold function and the threshold value on the filtering error caused by the noises of non-stationary measuring signals has been investigated by the method of a computational experiment. The results of the study of six threshold functions are given with the addition of noise to the measuring signal with nonstationary amplitude, frequency and duty cycle of rectangular pulses. The signal of the Doppler sensors is investigated, the wavelet filtering parameters are calculated, which provide the minimum error. The obtained parameters are used to construct graphs of signals before and after filtering directly in the time domain using the inverse wavelet transform.

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