The Wavelet Transform Spectrum and Random Wavelet Series With Applications to Fractional Brownian Motion
Wei, H.L. and Billings, S.A.
(2002)
The Wavelet Transform Spectrum and Random Wavelet Series With Applications to Fractional Brownian Motion.
Research Report.
ACSE Research Report 823
.
Department of Automatic Control and Systems Engineering
Abstract
The concepts of the wavelet transform spectrum (WTS) and random wavelet series (RWS) are introduced based on the continuous and discrete wavelet transforms. The relationship between the WTS and the ordinary power spectral density (PSD) function is derived. It follows that the WTS and the PSD of a wide-sense stationary process can be related by the Fourier transform of the associated wavelet. The spectrum of the associated wavelet. The spectrum of the well-known fractional Brownian motion (fBm) is derived by means of the global wavelet transform spectrum (GWTS). The second-order statistical characteristics of the RWS of fBm is analysed by adopting the Haar wavelet.
Metadata
Item Type:
Monograph
Authors/Creators:
Wei, H.L.
Billings, S.A.
Copyright, Publisher and Additional Information:
The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
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