A Space-Scale Estimation Method based on continuous wavelet transform for coastal wetland ecosystem services in Liaoning Province, China

2018 ◽  
Vol 157 ◽  
pp. 138-146
Author(s):  
Baodi Sun ◽  
Lijuan Cui ◽  
Wei Li ◽  
Xiaoming Kang ◽  
Manyin Zhang
Keyword(s):  
Wavelet Transform ◽  
Ecosystem Services ◽  
Continuous Wavelet Transform ◽  
Coastal Wetland ◽  
Estimation Method ◽  
Liaoning Province ◽  
Continuous Wavelet ◽  
Wetland Ecosystem ◽  
Scale Estimation ◽  
Space Scale

A meta-analysis of coastal wetland ecosystem services in Liaoning Province, China

2018 ◽  
Vol 200 ◽  
pp. 349-358 ◽  
Author(s):  
Baodi Sun ◽  
Lijuan Cui ◽  
Wei Li ◽  
Xiaoming Kang ◽  
Xu Pan ◽  
...  
Keyword(s):  
Ecosystem Services ◽  
Coastal Wetland ◽  
Meta Analysis ◽  
Liaoning Province ◽  
Wetland Ecosystem

scholarly journals Tacholess Rotational Speed Estimation via The Integration of Continuous Wavelet Transform and Time-Dependent Autoregression

2020 ◽  
Author(s):  
Ran Zhang ◽  
Xingxing Liu ◽  
Yongjun Zheng ◽  
Haotun Lv ◽  
Baosheng Li ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Estimation Method ◽  
Rotational Frequency ◽  
Time Dependent ◽  
Speed Estimation ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Vibration Sensors ◽  
Preprocessing Technique

Abstract Speed estimation is crucial to monitor the conditions of rotational machinery. Most speed measurements are carried out by installing encoders or tachometers inside the machines. In many cases, such method could be cumbersome or even inaccessible. This paper proposes a vibration-based speed estimation method. The vibration sensors are often cheaper and easier to install than angle encoders. In the proposed method, the continuous wavelet transform (CWT) is used as a preprocessing technique to extract the signal of importance. Then, the time-varying autoregressive (TAR) model is applied to analyze the rotational frequency. Additionally, the paper presents a fast algorithm for implementation. The proposed method is validated by both synthetic and empirical data.

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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