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Data Compression
Frequency Response
High Frequency
multiresolution analysis
Signal Extraction
Statistical Data Analysis
Wavelet Analysis
Fourier Transform
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Adapted Wavelet Analysis from Theory to Software
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NonDyadic Wavelet Analysis
NonDyadic Wavelet Analysis,10.1007/3540366261_9,Stephen Pollock,Iolanda Lo Cascio
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NonDyadic Wavelet Analysis
(
Citations: 7
)
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Stephen Pollock
,
Iolanda Lo Cascio
The conventional dyadic
multiresolution analysis
constructs a succession of frequency intervals in the form of (π/2 j , π/2 j1);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 nondyadic mixedradix
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
DOI:
10.1007/3540366261_9
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Citation Context
(4)
...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 Alexandrov
,
et 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 clickfraud attacks prevention...
...Pollock [
2
] generalizes dyadic packet WT technique, where the entire frequency range of the jth 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 Chertov
,
et al.
Nondyadic wavelets for detection of some clickfraud attacks
...Pollock [
20
] presents a nondyadic mixedradix wavelet analysis which allows the wave bands to be defined more flexibly than conventional dyadic basis...
Chetan Gupta
,
et al.
Nondyadic Haar wavelets for streaming and sensor data
...These di‐culties can be overcame by pursuing a MixedRadix WavePacket Analysissee
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 wavepacket 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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Citations
(7)
A Review of Some Modern Approaches to the Problem of Trend Extraction
(
Citations: 3
)
Theodore Alexandrov
,
Silvia Bianconcini
,
Estela Bee Dagum
,
Peter Maass
,
Tucker S. McElroy
Journal:
Econometric Reviews  ECONOM REV
, vol. justaccep, no. justaccep, 2012
Image and video upscaling from local selfexamples
Gilad Freedman
,
Raanan Fattal
Journal:
ACM Transactions on Graphics  TOG
, vol. 30, no. 2, pp. 111, 2011
Nondyadic wavelets for detection of some clickfraud attacks
Oleg Chertov
,
Volodymyr Malchykov
,
Dmytro Pavlov
Published in 2010.
Nondyadic Haar wavelets for streaming and sensor data
Chetan Gupta
,
Choudur Lakshminarayan
,
Song Wang
,
Abhay Mehta
Conference:
International Conference on Data Engineering  ICDE
, pp. 569580, 2010
Investigating Economic Trends And Cycles
(
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)
D. S. G. Pollock
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