A composite Fourier‐wavelet transform and square‐integrable group representations

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on ℝd.

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ECG signal feature extraction and classification using wavelet transform and neural network

PsycEXTRA Dataset ◽

10.1037/e605272012-004 ◽

2011 ◽

Author(s):

Thomas Sri Widodo

Keyword(s):

Neural Network ◽

Feature Extraction ◽

Wavelet Transform ◽

Ecg Signal

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Group Representations

10.1016/s0304-0208(09)x7004-0 ◽

1980 ◽

Keyword(s):

Group Representations

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Classification of Acceleration Waveforms during Walking by Wavelet Transform

Methods of Information in Medicine ◽

10.1055/s-0038-1636855 ◽

1997 ◽

Vol 36 (04/05) ◽

pp. 356-359 ◽

Cited By ~ 27

Author(s):

M. Sekine ◽

M. Ogawa ◽

T. Togawa ◽

Y. Fukui ◽

T. Tamura

Keyword(s):

Wavelet Transform ◽

Wavelet Analysis ◽

Center Of Gravity ◽

Dynamic Responses ◽

Sequential Data ◽

Acceleration Signal ◽

Continuous Dynamic

Abstract:In this study we have attempted to classify the acceleration signal, while walking both at horizontal level, and upstairs and downstairs, using wavelet analysis. The acceleration signal close to the body’s center of gravity was measured while the subjects walked in a corridor and up and down a stairway. The data for four steps were analyzed and the Daubecies 3 wavelet transform was applied to the sequential data. The variables to be discriminated were the waveforms related to levels -4 and -5. The sum of the square values at each step was compared at levels -4 and -5. Downstairs walking could be discriminated from other types of walking, showing the largest value for level -5. Walking at horizontal level was compared with upstairs walking for level -4. It was possible to discriminate the continuous dynamic responses to walking by the wavelet transform.

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Application of Wavelet Transform Analysis for Pavement Roughness Studies

Applications of Advanced Technologies in Transportation Engineering (2004) ◽

10.1061/40730(144)85 ◽

2004 ◽

Author(s):

Liu Wei ◽

T. F. Fwa

Keyword(s):

Wavelet Transform ◽

Pavement Roughness ◽

Wavelet Transform Analysis

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Adaptive identification methods of nonlinear random electrical signal

International Journal of Applied Electromagnetics and Mechanics ◽

10.3233/jae-209349 ◽

2020 ◽

Vol 64 (1-4) ◽

pp. 431-438

Author(s):

Jian Liu ◽

Lihui Wang ◽

Zhengqi Tian

Keyword(s):

Wavelet Transform ◽

Electric Vehicle ◽

Signal To Noise Ratio ◽

Sudden Change ◽

Electrical Signal ◽

Signal Recognition ◽

State Variable ◽

Signal Characteristics ◽

The Matrix ◽

Kalman Filter Algorithm

The nonlinearity of the electric vehicle DC charging equipment and the complexity of the charging environment lead to the complex and changeable DC charging signal of the electric vehicle. It is urgent to study the distortion signal recognition method suitable for the electric vehicle DC charging. Focusing on the characteristics of fundamental and ripple in DC charging signal, the Kalman filter algorithm is used to establish the matrix model, and the state variable method is introduced into the filter algorithm to track the parameter state, and the amplitude and phase of the fundamental waves and each secondary ripple are identified; In view of the time-varying characteristics of the unsteady and abrupt signal in the DC charging signal, the stratification and threshold parameters of the wavelet transform are corrected, and a multi-resolution method is established to identify and separate the unsteady and abrupt signals. Identification method of DC charging distortion signal of electric vehicle based on Kalman/modified wavelet transform is used to decompose and identify the signal characteristics of the whole charging process. Experiment results demonstrate that the algorithm can accurately identify ripple, sudden change and unsteady wave during charging. It has higher signal to noise ratio and lower mean root mean square error.

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