The Wavelet Transform Spectrum and Random Wavelet Series With Applications to Fractional Brownian Motion
Hu Wei, Stephen A. Billings · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 2002
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.