In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the recons...

This paper deals with nonuniform transmission lines which are excited at high frequencies. Networks of those lines are formed and they are described by the BLT–equation. The essential ingredients in this equation are the scattering and the propagation supermatrices. For our investigations we derive these quantities from the product integral solution of generalized telegrapher’s equations. The m...

This work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noises. Three main nonuniform filter bank systems, i.e., filter-block decimator (FBD) structure, upsamplerfilter-downsampler (UFD) structure, and tree structure, are included in this study. According to different operating conditions, two different signal reconstructi...

In some applications the observed samples are inherently nonuniform. In contrast to that in this paper we take advantage of deliberate nonuniform sampling and perform DSP where the classical approaches leave off. For instance think about mobile communication or digital radio. Deliberate nonuniform sampling promises increased equivalent sampling rates with reduced overall hardware costs. The equ...

Articular cartilage is critical to the normal function of diarthrodial joints. Despite the importance of the tissue and the prevalence of cartilage degeneration (e.g., osteoarthritis), the technology required to noninvasively describe nonuniform deformations throughout the volume of the tissue has not been available until recently. The objectives of the work reported in this paper were to 1) de...

The local reconstruction from samples is one of most desirable properties for many applications in signal processing, but it has not been given as much attention. In this paper, we will consider the local reconstruction problem for signals in a shiftinvariant space. In particular, we consider finding sampling sets X such that signals in a shift-invariant space can be locally reconstructed from ...

This article describes a new kind of processing chain based on a nonuniform sampling scheme provided by a level-crossing ADC. The chain implements IIR filters which process directly the non-uniform samples without resampling in a regular scheme. The non-uniformity in the sample times leads to choose a state representation for the filters. The stability is studied and the performances of various...

In this position paper, the roles of sampling rate, i.e. alternatively, sampling time, have been investigated in the receiver design of a concentration-encoded molecular communication (CEMC) system. While several signal detection algorithms so far in CEMC are based on uniform sampling of concentration intensity at the RN, this paper presents four new sampling rate selection schemes based on bot...

We establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness with lower randomness rate. More precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with cons...

The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in R which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element a...