This paper addresses a bias problem in the estimate of wavelet power spectra for atmospheric and oceanic datasets. For a time series comprised of sine waves with the same amplitude at different frequencies the conventionally adopted wavelet method does not produce a spectrum with identical peaks, in contrast to a Fourier analysis. The wavelet power spectrum in this definition, that is, the tran...

To optimize the number of decomposition layers in wavelet threshold denoising for ultrasonic signals, we propose a self-adaptive algorithm of determining the number of decomposition layers based on singular spectrum analysis and wavelet entropy. First the noise-containing signals are decomposed by discrete wavelet transform. The slope of the singular value spectrum for each layer is estimated. ...

In this paper, the use of wavelet analysis and artificial neural networks for generating artificial earthquake accelerograms from target spectrum is suggested as a new method. This procedure uses the learning capabilities of neural network to expand the knowledge of the inverse mapping from response spectrum to earthquake accelerogram. In the first step, wavelet analysis is used to decompose ea...

The relation between Fourier spectra and spectra obtained from wavelet analysis is established. Small scale asymptotic analysis shows that the wavelet spectrum is meaningful only when the analysing wavelet has enough vanishing moments. We relate these results to regularity theorems in Besov spaces. For the analysis of innnitly regular signals, a new wavelet, with innnit number of cancellations ...

In the past few years, wavelet methods have been applied in coastal and ocean current data analysis [2, 5, 6]. These new tools have better performance than the traditional Fourier techniques. They localize the information in the time-frequency space and are capable of trading one type of resolution for the other, which renders them suitable for the analysis of nonstationary signals. It was firs...

We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are deened by explicit coeecients on an orthonormal wavelet basis. We compute their HH older regularity and oscillation at every point and we deduce their spectrum of oscillating singularities.