CWT × DWT × DTWT × SDTWT: Clarifying terminologies and roles of different types of wavelet transforms

2020 ◽  
Vol 18 (06) ◽  
pp. 2030001 ◽  
Author(s):  
Rodrigo Capobianco Guido ◽  
Fernando Pedroso ◽  
André Furlan ◽  
Rodrigo Colnago Contreras ◽  
Luiz Gustavo Caobianco ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Discrete Time ◽  
Wavelet Transforms ◽  
Signal Analysis ◽  
Applied Mathematics ◽  
Discrete Wavelet ◽  
Frequency Signal ◽  
Time Frequency ◽  
Subsequent Investigation ◽  
Different Types

Wavelets have been placed at the forefront of scientific researches involving signal processing, applied mathematics, pattern recognition and related fields. Nevertheless, as we have observed, students and young researchers still make mistakes when referring to one of the most relevant tools for time–frequency signal analysis. Thus, this correspondence clarifies the terminologies and specific roles of four types of wavelet transforms: the continuous wavelet transform (CWT), the discrete wavelet transform (DWT), the discrete-time wavelet transform (DTWT) and the stationary discrete-time wavelet transform (SDTWT). We believe that, after reading this correspondence, readers will be able to correctly refer to, and identify, the most appropriate type of wavelet transform for a certain application, selecting relevant and accurate material for subsequent investigation.

scholarly journals Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Timur Düzenli ◽  
Nalan Özkurt
Keyword(s):  
Wavelet Transform ◽  
Real Time ◽  
Wavelet Transforms ◽  
Principal Component ◽  
Discrete Wavelet ◽  
Vanishing Moments ◽  
Zero Crossings ◽  
Time Frequency ◽  
Common Time ◽  
Classification Tool

The performance of wavelet transform-based features for the speech/music discrimination task has been investigated. In order to extract wavelet domain features, discrete and complex orthogonal wavelet transforms have been used. The performance of the proposed feature set has been compared with a feature set constructed from the most common time, frequency and cepstral domain features such as number of zero crossings, spectral centroid, spectral flux, and Mel cepstral coefficients. The artificial neural networks have been used as classification tool. The principal component analysis has been applied to eliminate the correlated features before the classification stage. For discrete wavelet transform, considering the number of vanishing moments and orthogonality, the best performance is obtained with Daubechies8 wavelet among the other members of the Daubechies family. The dual tree wavelet transform has also demonstrated a successful performance both in terms of accuracy and time consumption. Finally, a real-time discrimination system has been implemented using the Daubhecies8 wavelet which has the best accuracy.

Wavelet Transforms and Time-Frequency Signal Analysis

Technometrics ◽  
2002 ◽  
Vol 44 (1) ◽  
pp. 87-87
Author(s):  
Chris Chatfteld
Keyword(s):  
Wavelet Transforms ◽  
Signal Analysis ◽  
Frequency Signal ◽  
Time Frequency

New Evaluation Method on Gear Dynamics Using Continuous and Discrete Wavelet Transforms

2003 ◽  
Vol 125 (3) ◽  
pp. 274-281 ◽  
Author(s):  
Yuji Ohue ◽  
Akira Yoshida
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Evaluation Method ◽  
Dynamic Condition ◽  
Testing Machine ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Gear Dynamics ◽  
Time Frequency ◽  
The Difference

The aim of this study is to propose a new evaluation method of gear dynamics using the continuous and discrete wavelet transforms. The wavelet transform (WT) is a method for the time-frequency analysis of signals. In order to evaluate the difference in the gear dynamics due to the gear materials, which are sintered and steel ones, the dynamic characteristics of gears were measured using a power circulating gear testing machine. The gear dynamics were analyzed in a time-frequency domain by the continuous and discrete WTs. The new evaluation method using the WTs proposed in this paper was more useful compared with the conventional one to investigate the damping characteristic and the dynamic condition of the gear equipment.

scholarly journals Wavelet Theory and Application in Communication and Signal Processing

2021 ◽  
Author(s):  
Nizar Al Bassam ◽  
Vidhyalavanya Ramachandran ◽  
Sumesh Eratt Parameswaran
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Communication Systems ◽  
Orthogonal Frequency Division Multiplexing ◽  
Applied Mathematics ◽  
Multimedia Systems ◽  
Biomedical Signal Processing ◽  
Discrete Wavelet

Wavelet analysis is the recent development in applied mathematics. For several applications, Fourier analysis fails to provide tangible results due to non-stationary behavior of signals. In such situation, wavelet transforms can be used as a potential alternative. The book chapter starts with the description about importance of frequency domain representation with the concept of Fourier series and Fourier transform for periodic, aperiodic signals in continuous and discrete domain followed by shortcoming of Fourier transform. Further, Short Time Fourier Transform (STFT) will be discussed to induce the concept of time frequency analysis. Explanation of Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT) will be provided with the help of theoretical approach involving mathematical equations. Decomposition of 1D and 2D signals will be discussed suitable examples, leading to application concept. Wavelet based communication systems are becoming popular due to growing multimedia applications. Wavelet based Orthogonal Frequency Division Multiplexing (OFDM) technique and its merit also presented. Biomedical signal processing is an emerging field where wavelet provides considerable improvement in performance ranging from extraction of abnormal areas and improved feature extraction scheme for further processing. Advancement in multimedia systems together with the developments in wireless technologies demands effective data compression schemes. Wavelet transform along with EZW, SPIHT algorithms are discussed. The chapter will be a useful guide to undergraduate and post graduate who would like to conduct a research study that include wavelet transform and its usage.

scholarly journals Non-decimated Wavelet Transform for a Shift-invariant Analysis

2018 ◽  
Vol 19 (1) ◽  
pp. 93 ◽  
Author(s):  
Gabriela De Oliveira Nascimento Brassarote ◽  
Eniuce Menezes de Souza ◽  
João Francisco Galera Monico
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Signal Analysis ◽  
Perfect Reconstruction ◽  
Discrete Wavelet ◽  
Continuous Version ◽  
Time Frequency ◽  
Application Potential ◽  
Invariant Analysis ◽  
Analysis Of Time Series

Due to the ability of time-frequency location, the wavelet transform hasbeen applied in several areas of research involving signal analysis and processing,often replacing the conventional Fourier transform. The discrete wavelet transformhas great application potential, being an important tool in signal compression,signal and image processing, smoothing and denoising data. It also presentsadvantages over the continuous version because of its easy implementation, goodcomputational performance and perfect reconstruction of the signal upon inversion.Nevertheless, the downsampling required in the discrete wavelet transformcalculous makes it shift variant and not appropriated to some applications, suchas for signals or time series analysis. On the other hand, the Non-Decimated DiscreteWavelet Transform is shift-invariant because it eliminates the downsamplingand, consequently, is more appropriate for identifying both stationary and nonstationarybehaviors in signals. However, the non-decimated wavelet transform hasbeen underused in the literature. This paper intends to show the advantages ofusing the non-decimated wavelet transform in signal analysis. The main theoricaland pratical aspects of the multiscale analysis of time series from non-decimatedwavelets in terms of its formulation using the same pyramidal algorithm of thedecimated wavelet transform was presented. Finally, applications with a simulatedand real time series compare the performance of the decimated and non-decimatedwavelet transform, demonstrating the superiority of non-decimated one, mainly dueto the shift-invariant analysis, patterns detection and more perfect reconstructionof a signal.

New Evaluation Method on Gear Dynamics Using Continuous and Discrete Wavelet Transforms

2000 ◽  
Author(s):  
Yuji Ohue ◽  
Akira Yoshida
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Evaluation Method ◽  
Dynamic Condition ◽  
Testing Machine ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Gear Dynamics ◽  
Time Frequency ◽  
The Difference

Abstract The aim of this study is to propose a new evaluation method of gear dynamics using continuos and discrete wavelet transforms. The Wavelet Transform (WT) is a method for the time-frequency analysis of signals. In order to evaluate the difference in the gear dynamics due to the gear material, the dynamic characteristics of gear were measured using a power circulating gear testing machine. The gear dynamics were analyzed in a time-frequency domain by the continuos and discrete WTs. The new evaluation method using the WTs proposed in this paper was very useful compared with the conventional one to investigate the damping characteristic and the dynamic condition of the gear equipment.

Compressive Spectrum Sensing

2019 ◽  
pp. 203-228
Author(s):  
Said E. El-Khamy ◽  
Mina B. Abd el-Malek ◽  
Sara H. Kamel
Keyword(s):  
Wavelet Transform ◽  
Compressive Sensing ◽  
Spectrum Sensing ◽  
Wavelet Transforms ◽  
Auxiliary Function ◽  
Discrete Wavelet ◽  
Wideband Spectrum Sensing ◽  
Reconstruction Methods ◽  
Data Rates ◽  
Different Types

In this chapter, the authors discuss how compressive sensing can be used in wideband spectrum sensing in cognitive radio systems. Compressive sensing helps decrease the complexity and processing time and allows for higher data rates to be used, since it makes it possible for the signal to be sampled at rates lower than the Nyquist rate and still be reconstructed with high accuracy. Different sparsifying bases for compressive sensing are presented in this chapter and their performance is compared. The design of these matrices is based on different types of wavelet transforms, including the discrete wavelet transform and the stationary wavelet transform; the latter having shown a clear improvement in performance over the former. The authors present different ways of implementing these transforms in a compressive sensing framework. Additionally, different types of reconstruction methods including the genetic algorithm and the auxiliary function method are also presented and their impact on the overall performance is discussed.

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