Biorthogonal Wavelet Transforms Originating from Discrete and Discrete-Time Splines

2018 ◽  
pp. 133-147
Author(s):  
Amir Z. Averbuch ◽  
Pekka Neittaanmäki ◽  
Valery A. Zheludev
Keyword(s):  
Discrete Time ◽  
Wavelet Transforms ◽  
Biorthogonal Wavelet

Wavelet transforms for discrete-time periodic signals

1995 ◽  
Vol 42 (2) ◽  
pp. 167-180 ◽  
Author(s):  
John A. Gubner ◽  
Wei-Bin Chang
Keyword(s):  
Discrete Time ◽  
Wavelet Transforms ◽  
Periodic Signals ◽  
Time Periodic

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.

Image restoration using biorthogonal wavelet transforms

1994 ◽  
Vol 33 (7) ◽  
pp. 2378 ◽  
Author(s):  
Pierre Mathieu
Keyword(s):  
Image Restoration ◽  
Wavelet Transforms ◽  
Biorthogonal Wavelet

Rapid design of biorthogonal wavelet transforms

2000 ◽  
Vol 147 (5) ◽  
pp. 293 ◽  
Author(s):  
S. Masud ◽  
J.V. McCanny
Keyword(s):  
Wavelet Transforms ◽  
Biorthogonal Wavelet ◽  
Rapid Design

Fault Diagnosis of Gearbox Based on Wavelet Transforms and Neural Networks

2011 ◽  
Vol 148-149 ◽  
pp. 919-922
Author(s):  
Guang Bin Zhang ◽  
Yun Jian Ge ◽  
Yong Jiu Liu
Keyword(s):  
Neural Networks ◽  
Wavelet Transforms ◽  
Failure Diagnosis ◽  
Biorthogonal Wavelet ◽  
Actual System ◽  
Network Learning ◽  
Learning Speed ◽  
Vanishing Moment ◽  
Marquardt Algorithm ◽  
Different Types

In this paper, an actual system based on wavelet transform and artificial neural networks was established to diagnose different types of fault in a gearbox. As a key step, biorthogonal wavelet was used to denoise in feature extraction of signals because of its properties of compact support, high vanishing moment and symmetry. Consequently, a multi-layer perceptron network were designed to diagnose the fault status with feature vectors as inputs. In order to improve the network learning speed and stability, Levenberg-Marquardt algorithm was used to train the network. The present classification accuracy indicates the effectiveness of gearbox failure diagnosis.

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