arXiv subjects

Hans G. Feichtinger

Publications and source records attributed to Hans G. Feichtinger.

22 records · Page 2Linked to original sources

arXiv2009

Approximate reconstruction of bandlimited functions for the integrate and fire sampler

In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and is specially convenient in situations where the sampling device is limited in terms of power, area and bandwidth. Although perfect reconstruction for this sampler is impossible, we give a general approximate reconstruction procedure and bound the corresponding error. We also show the performance of the proposed algorithm through numerical simulations.

physics.data-an↗

arXiv2005

Minimal Norm Interpolation in Harmonic Hilbert Spaces and Wiener Amalgam Spaces on Locally Compact Abelian Groups

The family of harmonic Hilbert spaces is a natural enlargement of those classical $L^{2}$-Sobolev space on $\R^d$ which consist of continuous functions. In the present paper we demonstrate that the use of basic results from the theory of Wiener amalgam spaces allows to establish fundamental properties of harmonic Hilbert spaces even if they are defined over an arbitrary locally compact abelian group $\G$. Even for $\G = \R^{d}$ this new approach improves previously known results. In this paper we present results on minimal norm interpolators over lattices and show that the infinite minimal norm interpolations are the limits of finite minimal norm interpolations. In addition, the new approach paves the way for the study of stability problems and error analysis for norm interpolations in harmonic Hilbert and Banach spaces on locally compact abelian groups.

math.FA↗

arXiv2002

Compactness Criteria in Function Spaces

The classical criterion for compactness in Banach spaces of functions can be reformulated into a simple tightness condition in the time-frequency domain. This description preserves more explicitly the symmetry between time and frequency than the classical conditions. The result is first stated and proved for L^2(R^d), and then generalized to coorbit spaces. As special cases, we obtain new characterizations of compactness in Besov-Triebel-Lizorkin spaces, modulation spaces and Bargmann-Fock spaces.

math.FA↗

arXiv1997

Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent $α$, which may be estimated for any FSPP or FRSPP by using a variety of statistical methods. Simulated FSPPs and FRSPPs consistently exhibit bias in this fractal exponent, however, rendering the study and analysis of these processes non-trivial. In this paper, we examine the synthesis and estimation of FRSPPs by carrying out a systematic series of simulations for several different types of FRSPP over a range of design values for $α$. The discrepancy between the desired and achieved values of $α$ is shown to arise from finite data size and from the character of the point-process generation mechanism. In the context of point-process simulation, reduction of this discrepancy requires generating data sets with either a large number of points, or with low jitter in the generation of the points. In the context of fractal data analysis, the results presented here suggest caution when interpreting fractal exponents estimated from experimental data sets.

adap-org↗