Related papers: On causal band-limited mean square approximation
The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested. These filters approximate the gain decay for some non-causal…
We establish an $L_1$-bound between the coefficients of the optimal causal filter applied to the data-generating process and its finite sample approximation. Here, we assume that the data-generating process is a second-order stationary time…
Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…
The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish predictability of…
Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown that all band-limited…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…
A continuous-time graph signal can be viewed as a time series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. Therefore, such a signal can be considered as a function on two domains: the…
This paper investigates the active sampling for estimation of approximately bandlimited graph signals. With the assistance of a graph filter, an approximately bandlimited graph signal can be formulated by a Gaussian random field over the…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
The paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e. without probabilistic assumptions. The method requires to solve a…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
An agent in a nonstationary contextual bandit problem should balance between exploration and the exploitation of (periodic or structured) patterns present in its previous experiences. Handcrafting an appropriate historical context is an…
We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions…
Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…