scholarly journals Wavelet transform and orthogonal decomposition of space $L^2$ on the Cartan domain $BDI(q=2)$

1997 ◽  
Vol 349 (5) ◽  
pp. 2049-2068 ◽  
Author(s):  
Qingtang Jiang
Keyword(s):  
Wavelet Transform ◽  
Orthogonal Decomposition ◽  
Cartan Domain

Flow field around a vibrating cantilever: coherent structure eduction by continuous wavelet transform and proper orthogonal decomposition

2011 ◽  
Vol 669 ◽  
pp. 584-606 ◽  
Author(s):  
Y.-H. KIM ◽  
C. CIERPKA ◽  
S. T. WERELEY
Keyword(s):  
Wavelet Transform ◽  
Proper Orthogonal Decomposition ◽  
Continuous Wavelet Transform ◽  
Vector Fields ◽  
Three Dimensional ◽  
Orthogonal Decomposition ◽  
Continuous Wavelet ◽  
Vortical Structures ◽  
Flow Features ◽  
Proper Orthogonal

The velocity field around a vibrating cantilever plate was experimentally investigated using phase-locked particle image velocimetry. Experiments were performed at Reynolds numbers of Reh = 101, 126 and 146 based on the tip amplitude and the speed of the cantilever. The averaged vector fields indicate a pseudo-jet flow, which is dominated by vortical structures. These vortical structures are identified and characterized using the continuous wavelet transform. Three-dimensional flow features are also clearly revealed by this technique. Furthermore, proper orthogonal decomposition was used to investigate regions of vortex production and breakdown. The results show clearly that the investigation of phase-averaged data hides several key flow features. Careful data post-processing is therefore necessary to investigate the flow around the vibrating cantilever and similar highly transient periodic flows.

Classification of Acceleration Waveforms during Walking by Wavelet Transform

1997 ◽  
Vol 36 (04/05) ◽  
pp. 356-359 ◽  
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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