As a general and rigid mathematical tool, wavelet theory has found many applications is constantly developing. This article reviews the development history of theory, from construction method to discussion properties. Then it focuses on design expansion transform. The main models algorithms transform are discussed. rational (RWT) provided by examples emphasizing advantages RWT over traditional ...

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can't be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis...

In the mid-1980's, wavelet theory was developed in applied mathematics [1, 2, 3]. Soon, subband coding [4], which has been a very active research area for image and video compression, was identi ed as wavelet's discrete cousin. Furthermore, a fundamental insight into the structure of subband lters was developed from wavelet theory that led to a more productive approach to designing the lters [1...

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image pro...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

Wavelet theory is an attempt to address the pervasive problem of describing the frequency content of a function locally in time. The wavelet approach is to analyze a function using an appropriate family of dilates and translates of one or more wavelets. Although this term is relatively new, wavelet-like techniques have been independently invented over the past 30 years in harmonic analysis, qua...

The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatial L2 R2 , proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale space L2 R2;H , and studies quaternion wavelet transform structure. Fina...

In this paper, we apply wavelet thresholding for removing automatically ground and intermittent clutter (airplane echoes) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop wavelet domain thresholding rules, which allow us to identify the coefficients relevant for clutter and to suppress them in order to obtain...

We have used wavelets and wavelet packets to analyse, model and compute turbulent flows. The theory and open questions encountered in turbulence are presented. The wavelet-based techniques that we have developed to study turbulence are explained and the main results are summarized.