Passive wideband cross correlation with differential Doppler compensation using the continuous wavelet transform

1999 ◽  
Vol 106 (6) ◽  
pp. 3434-3444 ◽  
Author(s):  
Brian G. Ferguson ◽  
Kam W. Lo
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Cross Correlation ◽  
Continuous Wavelet ◽  
Differential Doppler ◽  
Doppler Compensation

scholarly journals Application of an Automatic Noise or Signal Removal Algorithm Based on Synchrosqueezed Continuous Wavelet Transform of Passive Surface Wave Imaging: A Case Study in Sichuan, China

2021 ◽  
Vol 11 (24) ◽  
pp. 11718
Author(s):  
Jie Fang ◽  
Guofeng Liu ◽  
Yu Liu
Keyword(s):  
Wavelet Transform ◽  
Surface Wave ◽  
Surface Waves ◽  
Continuous Wavelet Transform ◽  
Cross Correlation ◽  
Underground Structure ◽  
Inversion Method ◽  
Continuous Wavelet ◽  
Dispersion Measurement ◽  
Wave Imaging

Passive surface wave imaging based on noise cross-correlation has been a research hotspot in recent years. However, because randomness of noise is difficult to achieve in reality, prominent noise sources will inevitably affect the dispersion measurement. Additionally, in order to recover high-fidelity surface waves, the time series input during cross-correlation calculation is usually very long, which greatly limits the efficiency of passive surface wave imaging. With an automatic noise or signal removal algorithm based on synchrosqueezed continuous wavelet transform (SS-CWT), these problems can be alleviated. We applied this method to 1-h passive datasets acquired in Sichuan province, China; separated the prominent noise events in the raw field data, and enhanced the cross-correlation reconstructed surface waves, effectively improving the accuracy of the dispersion measurement. Then, using the conventional surface wave inversion method, the shear wave velocity profile of the underground structure in this area was obtained.

IDENTIFICATION OF ROTATING PRESSURE WAVES IN A CENTRIFUGAL COMPRESSOR DIFFUSER BY MEANS OF THE WAVELET CROSS-CORRELATION

2006 ◽  
Vol 04 (02) ◽  
pp. 373-382 ◽  
Author(s):  
LONGIN HORODKO
Keyword(s):  
Correlation Function ◽  
Wavelet Transform ◽  
Centrifugal Compressor ◽  
Continuous Wavelet Transform ◽  
Signal Analysis ◽  
Cross Correlation ◽  
Rotating Stall ◽  
Pressure Waves ◽  
Continuous Wavelet ◽  
Compressor Impeller

Rotating stall is usually the first symptom of approaching compressor instability. It consists of zones of a turbulent flow, which rotate slower than the compressor impeller. The wavelet cross-correlation function was applied to detect rotating objects, whereas the continuous wavelet transform was used to identify different phases of the compressor operation. These methods of signal analysis enabled the identification of rotating pressure waves that appear during all phases of operation. Some of them have several times shorter wavelength than these manifested by the rotating stall. What is more, rotating pressure waves, though very weak, appear also during the stable compressor operation.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

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