Related papers: Higher-Order Properties of Analytic Wavelets
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
We have studied the characteristic timescales of 80 AGNs at 22, 37 and 90 GHz examining the properties of the wavelet method and comparing them to traditional Fourier-based methods commonly used in astronomy. We used the continuous wavelet…
A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized "events". Here these events are taken to be well represented as rescaled and phase-rotated versions of generalized…
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared to the classification of individual sizes…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
Aims. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for…
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
High frequency wind time series measured at different heights from the ground (from 1.5 to 25.5 meters) in an urban area were investigated by using the variance of the coefficients of their wavelet transform. Two ranges of scales were…
In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…
The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial…
This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
This work revisits a class of biomimetically inspired log-periodic waveforms first introduced by R.A. Altes in the 1970s for generalized target description. It was later observed that there is a close connection between such sonar…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery…