Related papers: An Optimal Weighting Function for the Savitzky-Gol…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
We determine the transfer functions of two kinds of filters that can be used in the detection of continuous gravitational radiation. The first one optimizes the signal-to-noise ratio, and the second reproduces the wave with minimum error.…
Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…
A Wiener filter can be interpreted as a cascade of a whitening- and an estimation filter. This paper gives a detailed investigates of the properties of these two filters. Then the practical consequences for the overall Wiener filter are…
The problem of the optimal allocation (in the expected mean square error sense) of a measurement budget for particle filtering is addressed. We propose three different optimal intermittent filters, whose optimality criteria depend on the…
In the last few years, the notion of optimal polynomial approximant has appeared in the mathematics literature in connection with Hilbert spaces of analytic functions of one or more variables. In the 70s, researchers in engineering and…
The sinc function is often used as the basis for the design of discrete linear-phase FIR filters. However the Fourier transform of the truncated sinc function exhibits ripple in the pass band due to the Gibbs phenomenon. This paper…
Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…
This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…
Smoothing algorithms for state-space models, i.e., fixed-interval smoothing, fixed-lag smoothing, and two-filter formula for smoothing, are examined using real examples. For linear and Gaussian state-space models, it is observed that…
Optimization-based filtering smoothes an image by minimizing a fidelity function and simultaneously preserves edges by exploiting a sparse norm penalty over gradients. It has obtained promising performance in practical problems, such as…
Stochastic texture filtering (STF) has re-emerged as a technique that can bring down the cost of texture filtering of advanced texture compression methods, e.g., neural texture compression. However, during texture magnification, the swapped…
Along with the development of interferometric gravitational wave detector, we enter into an epoch of gravitational wave astronomy, which will open a brand new window for astrophysics to observe our universe. Almost all of the data analysis…
The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated…
Filtering of digital signals is accomplished on an Excel spreadsheet using fast Fourier transform (FFT) convolution in which the kernel is either a Gaussian or a cosine modulated Gaussian. Pedagogical examples of low-pass and band-pass…
We investigate how bounds of resonance counting functions for Schottky surfaces behave under transitions to covering surfaces of finite degree. We consider the classical resonance counting function asking for the number of resonances in…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
We consider one-dimensional model of the interaction between surface and the internal gravity water waves. The internal wave is modeled by its basic form: a non-dispersive field with a horizontal current that is uniform over all depth,…
This work focuses on the critical aspect of accurate weight computation during the measurement incorporation phase of Gaussian mixture filters. The proposed novel approach computes weights by linearizing the measurement model about each…
In deep learning, stochastic gradient descent (SGD) and its momentum-based variants are widely used for optimization. However, the internal dynamics of these methods remain underexplored. In this paper, we analyze gradient behavior through…