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Non-Dyadic Wavelet Analysis

Non-Dyadic Wavelet Analysis,10.1007/3-540-36626-1_9,Stephen Pollock,Iolanda Lo Cascio

Non-Dyadic Wavelet Analysis   (Citations: 7)
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The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of (π/2 j , π/2 j-1);j = 1, 2, …, j of which the bandwidths are halved repeatedly in the descent from high frequencies to low frequencies. Whereas this scheme provides an excellent framework for encoding and transmitting signals with a high degree of data compression, it is less appropriate to statistical data analysis. A non-dyadic mixed-radix wavelet analysis which allows the wave bands to be defined more flexibly than in the case of a conventional dyadic analysis is described. The wavelets that form the basis vectors for the wave bands are derived from the Fourier transforms of a variety of functions that specify the frequency responses of the filters corresponding to the sequences of wavelet coefficients
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    • ...However, recent works, see (Bakshi and Stephanopoulos, 1994; Bakhtazad et al, 2000; Partal and Kuecuek, 2006; Tona et al, 2005; Vedam and Venkatasubramanian, 1997) in engineering literature and (Pollock and Lo Cascio, 2007) for an econometric viewpoint, revealed their potential in trend research...

    Theodore Alexandrovet al. A Review of Some Modern Approaches to the Problem of Trend Extraction

    • ...It means that nondyadic WT provides more precise signal component separation [2], just like in case of some click-fraud attacks prevention...
    • ...Pollock [2] generalizes dyadic packet WT technique, where the entire frequency range of the j-th step is divided into 2 j equal intervals...
    • ...Pollok proposes [2] to choose the sequence in descending order, as it minimizes the number of multiplication operations required in the process of filters construction...

    Oleg Chertovet al. Non-dyadic wavelets for detection of some click-fraud attacks

    • ...Pollock [20] presents a non-dyadic mixedradix wavelet analysis which allows the wave bands to be defined more flexibly than conventional dyadic basis...

    Chetan Guptaet al. Non-dyadic Haar wavelets for streaming and sensor data

    • ...These di‐culties can be overcame by pursuing a Mixed-Radix Wave-Packet Analysis|see Pollock and Lo Cascio, (2006)|which can be applied to sample sizes with arbitrary factorisations and can be seen as an extension of the dyadic wave-packet analysis (Wickerhauser, 1994)...
    • ...In particular, it owes its efflciency to the manner in which each bandpass can be constructed from elementary component fllters (Pollock and Lo Cascio, 2006) and is faster (O(N)) than the Fast Fourier Transform algorithm O(N log2 N). It can be recognised that, once the fllter H = fhkgL¡1 k=0 has been chosen, it completely determines ` and ˆ. Indeed, there focus of the DWT is upon the computation of wavelet amplitude coe‐cients rather ...

    Iolanda Lo Cascio. Wavelet Analysis and Denoising: New Tools for Economists

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