We consider semiparametric estimation of memory parameter in long memory stochastic volatility models. It is known that log periodogram regression estimator by Geweke and Porter-Hudak (1983) results in significant negative bias due to the existence of the spectrum of non-Gaussian noise process. Through wavelet transform of the squared process, we effectively remove the noise spectrum around zer...

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this Letter we show that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in the associated wavelet basis. The resulti...

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, ...

| A multiple access communication scheme using wavelet-based orthogonal codes is described. The message bit stream in each channel is encoded as a sequence of time-shifted replicates of a mother wavelet symbol at a particular scale. Diierent channels use the same wavelet symbol but a diierent scale. The messages are decod-able if the time-shifted and dilated replicates of the wavelet symbol use...

In this work we deene and study a new class of non{stationary random processes which are characterized by a representation with respect to a family of localized basis functions. Using non{decimated or \stationary" wavelets this generalizes the Cram er (Fourier) spectral representation of stationary time series. We provide a time{scale instead of a time{frequency decomposition and, hence, instea...

The process of calculating the effective values of voltage and current root mean square (RMS) using Fourier transform (FT) suffers a high computational effort. Since it provides only an amplitude-frequency spectrum, looses time-related information, and is unable to deal with no stationary waveforms, standard definitions are reformulated in the time-frequency domain using the wavelet transform (...

Wavelet transformation was applied as a noise elimination method of an amperometric algal biosensor. The drift of the baseline current was clearly removed by using the wavelet transformation. The S/N ratio, calculated by the power spectrum density, is about 3-times larger than that calculated by the current response. The response to a herbicide, atrazine, calculated from the power spectrum d...

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet pow...