The Generalized Wavelets Based on Meyer Wavelet

Abstract A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in L2(ℝd). While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct Latin square wavelets as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.

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Adaptive Meyer wavelet filters for machinery fault diagnosis based on harmonic infinite-taxicab norm and grasshopper optimization algorithm

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220971663 ◽

2020 ◽

pp. 095440622097166

Author(s):

Zhenling Mo ◽

Heng Zhang ◽

Jinglin Wang ◽

Jianyu Wang ◽

Hongyong Fu ◽

...

Keyword(s):

Fault Diagnosis ◽

Optimization Algorithm ◽

Band Pass Filter ◽

Pass Filter ◽

Low Pass Filter ◽

Wavelet Filters ◽

Empirical Wavelet Transform ◽

Grasshopper Optimization Algorithm ◽

Grasshopper Optimization ◽

Meyer Wavelet

Meyer wavelet filters are the key building blocks of empirical wavelet transform. In mechanical fault diagnosis, however, the boundaries of Meyer wavelet filters are usually defined empirically. In order to solve the problems, this paper proposes a new index called harmonic infinite-taxicab norm to guide grasshopper optimization algorithm to primarily optimize a band-pass filter and thus, concurrently and secondarily optimize a low-pass filter and a high-pass filter of Meyer wavelet. The proposed index is inspired by spectral Lp/Lq norm and it is closely related to fault characteristic frequency of rotating machinery. In addition, only three Meyer wavelet filters are demanded in each iteration of optimization. The effectiveness of the proposed method is validated by comparing with fast kurtogram method on analyzing faulty bearing data and gearbox data.

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An Effective Method to Denoiseeeg, ECG and PPG Signals based on Meyer Wavelet Transform

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i3.34.19415 ◽

2018 ◽

Vol 7 (3.34) ◽

pp. 678

Author(s):

P Thamarai ◽

Dr K.Adalarasu

Keyword(s):

Wavelet Transform ◽

Adaptive Filter ◽

Wavelet Decomposition ◽

Motion Artifact ◽

Signal Quality ◽

Frequency Noise ◽

Meyer Wavelet ◽

Discrete Transform ◽

Reference Input

In this analysis, the prevailing role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the constant and the discrete transform are considered in turn.A Wavelet denoising is functional on the original signal to eradicate high frequency noise, and then a process based on Meyer wavelet transform combined with adaptive filter is functional to eradicate the motion artifact. This approach uses Meyer Wavelet decomposition to extract the motion artifact, which is subsequently utilized as the reference input of an adaptive filter for noise cancellation. The technique diminishes the overhead of the circuit because it does not need a separate collection of reference input signal which link to noise. Testing results illustrate that this approach can efficiently remove motion artifact and make better the signal quality.

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Multiple Discolored Cyclic Harmonic Ratio Diagram Based on Meyer Wavelet Filters for Rotating Machine Fault Diagnosis

IEEE Sensors Journal ◽

10.1109/jsen.2019.2957413 ◽

2020 ◽

Vol 20 (6) ◽

pp. 3132-3141 ◽

Cited By ~ 7

Author(s):

Chong Luo ◽

Zhenling Mo ◽

Jianyu Wang ◽

Jing Jiang ◽

Wenxin Dai ◽

...

Keyword(s):

Fault Diagnosis ◽

Wavelet Filters ◽

Rotating Machine ◽

Machine Fault Diagnosis ◽

Machine Fault ◽

Meyer Wavelet ◽

Harmonic Ratio

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On the uncertainty principle for Meyer wavelet functions

Journal of Mathematical Sciences ◽

10.1007/s10958-012-0770-y ◽

2012 ◽

Vol 182 (5) ◽

pp. 656-662 ◽

Cited By ~ 3

Author(s):

E. A. Lebedeva

Keyword(s):

Uncertainty Principle ◽

Meyer Wavelet

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Identification of Faults in Parallel Transmission Lines Using Discrete Meyer Wavelet

2020 IEEE 5th International Conference on Computing Communication and Automation (ICCCA) ◽

10.1109/iccca49541.2020.9250831 ◽

2020 ◽

Author(s):

Gaurav Kapoor ◽

Rabindra Nath Shaw

Keyword(s):

Transmission Lines ◽

Parallel Transmission ◽

Meyer Wavelet

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Flow Measurement Wavelet Filtering for Ultrasonic Flow Meter

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.390.445 ◽

2013 ◽

Vol 390 ◽

pp. 445-449

Author(s):

Yu Yang ◽

Wen Wen ◽

Guang Hua Zong ◽

Feng Lin Ding ◽

Yong Li

Keyword(s):

Integrated Circuit ◽

Digital Signal ◽

Power Input ◽

Haar Wavelet ◽

Noise Sources ◽

Flow Meter ◽

Wavelet Filtering ◽

Wavelet Filters ◽

Ultrasonic Flow Meter ◽

Meyer Wavelet

This paper introduces the wavelet filtering to the digital signal processing of ultrasonic flow meter. The noise sources in ultrasonic flow meter are analyzed, and they are divided into three groups: power input, integrated circuit, and other acoustic ways. Some of the noise is not white noise, so traditional noise reduction filter is not effective. Original signal from ultrasonic flow meter is sampled, and four wavelet filters (Haar wavlet, Daubechies wavelet, Symlets wavlet, and discrete Meyer wavelet) with three threshold methods (SURE threshold, Universal threshold, and Minimax threshold) on the signal is compared through experiment. The result shows Haar wavelet with Universal threshold has the best filtering ability for ultrasonic flow meter.

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