相关论文: Wavelet Based Time Series Models with Time-Varying…

In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…

Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of…

We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the…

Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…

A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…

We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy…

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…

A new method for solving optimal tracking control of linear quadratic time-varying systems with multiple time delays in state and input variables and with combined constraints is presented in this paper. By using the relations of Chebyshev…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

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.…

The Multiscale Fourier Transform of a seismic trace performs time-frequency analyses over a range of window lengths. The variation in window length captures local and global relative amplitudes between events, thereby allowing reflectivity…

In this paper, we study the problem of estimation and learning under temporal distribution shift. Consider an observation sequence of length $n$, which is a noisy realization of a time-varying groundtruth sequence. Our focus is to develop…

How to best develop foundational models for time series forecasting remains an important open question. Tokenization is a crucial consideration in this effort: what is an effective discrete vocabulary for a real-valued sequential input? To…

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…

Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…

We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…

Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…

A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al.…

Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…

Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…