scholarly journals Non-Separable Linear Canonical Wavelet Transform

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2182
Author(s):  
Hari M. Srivastava ◽  
Firdous A. Shah ◽  
Tarun K. Garg ◽  
Waseem Z. Lone ◽  
Huzaifa L. Qadri
Keyword(s):  
Wavelet Transform ◽  
Preliminary Analysis ◽  
Integral Transform ◽  
The Novel ◽  
Time Frequency ◽  
Fundamental Properties ◽  
Canonical Domain ◽  
Frequency Representation ◽  
Higher Dimensional ◽  
Uncertainty Inequalities

This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion of a non-separable linear canonical wavelet transform in L2(Rn). The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, we formulate several uncertainty inequalities, including the Heisenberg’s, logarithmic, and Nazorav’s inequalities for the proposed transform in the linear canonical domain. The obtained results are reinforced with illustrative examples.

scholarly journals Fall Detection Using Multiple Bioradars and Convolutional Neural Networks

Sensors ◽  
2019 ◽  
Vol 19 (24) ◽  
pp. 5569 ◽  
Author(s):  
Lesya Anishchenko ◽  
Andrey Zhuravlev ◽  
Margarita Chizh
Keyword(s):  
Wavelet Transform ◽  
Input Data ◽  
Detection Method ◽  
Fall Detection ◽  
Modern Medicine ◽  
Radar Signal ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Frequency Representation ◽  
Life Threatening

A lack of effective non-contact methods for automatic fall detection, which may result in the development of health and life-threatening conditions, is a great problem of modern medicine, and in particular, geriatrics. The purpose of the present work was to investigate the advantages of utilizing a multi-bioradar system in the accuracy of remote fall detection. The proposed concept combined usage of wavelet transform and deep learning to detect fall episodes. The continuous wavelet transform was used to get a time-frequency representation of the bio-radar signal and use it as input data for a pre-trained convolutional neural network AlexNet adapted to solve the problem of detecting falls. Processing of the experimental results showed that the designed multi-bioradar system can be used as a simple and view-independent approach implementing a non-contact fall detection method with an accuracy and F1-score of 99%.

Wavelet transform with generalized beta wavelets for seismic time-frequency analysis

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. O47-O56 ◽  
Author(s):  
Zhiguo Wang ◽  
Bing Zhang ◽  
Jinghuai Gao ◽  
Qingzhen Wang ◽  
Qing Huo Liu
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Seismic Data ◽  
Significant Information ◽  
Trade Off ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Reflection Seismic ◽  
Seismic Waveform ◽  
Frequency Representation

Using the continuous wavelet transform (CWT), the time-frequency analysis of reflection seismic data can provide significant information to delineate subsurface reservoirs. However, CWT is limited by the Heisenberg uncertainty principle, with a trade-off between time and frequency localizations. Meanwhile, the mother wavelet should be adapted to the real seismic waveform. Therefore, for a reflection seismic signal, we have developed a progressive wavelet family that is referred to as generalized beta wavelets (GBWs). By varying two parameters controlling the wavelet shapes, the time-frequency representation of GBWs can be given sufficient flexibility while remaining exactly analytic. To achieve an adaptive trade-off between time-frequency localizations, an optimization workflow is designed to estimate suitable parameters of GBWs in the time-frequency analysis of seismic data. For noise-free and noisy synthetic signals from a depositional cycle model, the results of spectral component using CWT with GBWs display its flexibility and robustness in the adaptive time-frequency representation. Finally, we have applied CWT with GBWs on 3D seismic data to show its potential to discriminate stacked fluvial channels in the vertical sections and to delineate more distinct fluvial channels in the horizontal slices. CWT with GBWs provides a potential technique to improve the resolution of exploration seismic interpretation.

ON THE USE OF THE REASSIGNED WAVELET TRANSFORM FOR MODE IDENTIFICATION

2004 ◽  
Vol 12 (02) ◽  
pp. 175-196 ◽  
Author(s):  
MICHAEL I. TAROUDAKIS ◽  
GEORGE TZAGKARAKIS
Keyword(s):  
Wavelet Transform ◽  
Shallow Water ◽  
Underwater Acoustics ◽  
Low Frequency ◽  
Energy Concentration ◽  
Propagation Mode ◽  
Mode Identification ◽  
Time Frequency ◽  
Frequency Representation ◽  
Calculation Point

This paper is concerned with the use of the reassigned wavelet transform for mode identification in shallow water acoustic propagation. Mode identification is important for inverse procedures in underwater acoustics. An efficient way to recognize the modal structure of the acoustic field when a single hydrophone is available is to refer to the time frequency analysis of the recorded signal using wavelet transform. However, the standard wavelet transform in some cases may result in an obscure representation of the dispersion curves. Thus, a reassigned process is proposed which brings important improvements in the time frequency representation of the signal. This is achieved by moving the calculation point of the scalogram in the center of gravity of the energy concentration, associated with each one of the propagating modes. This argument is supported by two illustrative examples corresponding to propagation of low frequency tomographic signals, in shallow water.

scholarly journals An Intertwining of Curvelet and Linear Canonical Transforms

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Azhar Y. Tantary ◽  
Firdous A. Shah
Keyword(s):  
Preliminary Analysis ◽  
Degrees Of Freedom ◽  
Curvelet Transform ◽  
Fundamental Question ◽  
The Novel ◽  
Reconstruction Formula ◽  
Fundamental Properties ◽  
Fundamental Relationship ◽  
Heisenberg Type ◽  
Discrete Analogues

In this article, we introduce a novel curvelet transform by combining the merits of the well-known curvelet and linear canonical transforms. The motivation towards the endeavour spurts from the fundamental question of whether it is possible to increase the flexibility of the curvelet transform to optimize the concentration of the curvelet spectrum. By invoking the fundamental relationship between the Fourier and linear canonical transforms, we formulate a novel family of curvelets, which is comparatively flexible and enjoys certain extra degrees of freedom. The preliminary analysis encompasses the study of fundamental properties including the formulation of reconstruction formula and Rayleigh’s energy theorem. Subsequently, we develop the Heisenberg-type uncertainty principle for the novel curvelet transform. Nevertheless, to extend the scope of the present study, we introduce the semidiscrete and discrete analogues of the novel curvelet transform. Finally, we present an example demonstrating the construction of novel curvelet waveforms in a lucid manner.

Empirical Wavelet Transform; Stationary and Nonstationary Signals

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Sedigheh Ghofrani
Keyword(s):  
Wavelet Transform ◽  
Digital Signal ◽  
Signal Decomposition ◽  
Early Nineteenth Century ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Frequency Representation ◽  
Empirical Wavelet Transform ◽  
Frequency Components ◽  
The Relationship

Signal decomposition into the frequency components is one of the oldest challenges in the digital signal processing. In early nineteenth century, Fourier transform (FT) showed that any applicable signal can be decomposed by unlimited sinusoids. However, the relationship between time and frequency is lost under using FT. According to many researches for appropriate time-frequency representation, in early twentieth century, wavelet transform (WT) was proposed Wavelet transform (WT) is a well-known method which developed in order to decompose a signal into frequency components. In contrast with original WT which is not adaptive according to the input signal, empirical wavelet transform (EWT) was proposed to overcome this problem. In this paper, the performance of WT and EWT in terms of signal decomposing into basic components are compared. For this purpose, a stationary signal include five sinusoids and ECG as biomedical and nonstationary signal are used. Due to being non-adaptive, WT may remove signal components but EWT because of being adaptive is appropriate. EWT can also extract the baseline of ECG signal easier than WT.

Extension of Traditional Frequency and Research on Time-Frequency Distribution

2010 ◽  
Vol 44-47 ◽  
pp. 2089-2093
Author(s):  
Shu Lin Liu ◽  
Xian Ming Wang ◽  
Hui Wang ◽  
Hai Feng Zhao
Keyword(s):  
Wavelet Transform ◽  
Frequency Distribution ◽  
Frequency Analysis ◽  
Physical Meaning ◽  
The Novel ◽  
Analysis Method ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Novel Approach ◽  
Time Frequency Distribution

The concept of traditional frequency is extended and the concept of local frequency is proposed, which makes the physical meaning of frequency clearer. The wide adaptability of local frequency is also discussed. Moreover, a novel time-frequency analysis method is presented based on local frequency. The time-frequency distribution of continuous triangular wave signal is analyzed by the novel approach. Compared with wavelet transform and Hilbert-Huang transform (HHT), the results show that the concept of local frequency is correct and the novel time-frequency approach is effective.

Applications of the synchrosqueezing transform in seismic time-frequency analysis

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. V55-V64 ◽  
Author(s):  
Roberto H. Herrera ◽  
Jiajun Han ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Seismic Signals ◽  
Time Frequency ◽  
Trade Offs ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Synchrosqueezing Transform ◽  
Instantaneous Frequencies

Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight individual components. We introduce the SST with applications for seismic signals and produced promising results on synthetic and field data examples.

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