We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique du...

This paper proves that every frame of windowed exponentials satisfies a Strong Homogeneous Approximation Property with respect to its canonical dual frame, and a Weak Homogeneous Approximation Property with respect to an arbitrary dual frame. As a consequence, a simple proof of the Nyquist density phenomenon satisfied by frames of windowed exponentials with one or finitely many generators is ob...

Multiple frame prediction has proved successful in increasing the performance of motion compensated video coders. Region-of-interest (ROI) coding in conjunction with a dual frame predictor can lead to interesting design choices on how to allocate the available bitrate among the frame regions. In this work, we tackle the problem of applying ROI coding on aerial imagery and then on standard video...

Data from complex survey designs require special consideration with regard to estimation of finite population parameters and corresponding variance estimation procedures, as a consequence of significant departures from the simple random sampling assumption. In the past decade a number of statistical software packages have been developed to facilitate the analysis of complex survey data. All the...

Dual frame surveys, in which independent samples are selected from two frames to decrease survey costs or to improve coverage, can present challenges for regression coefficient estimation because of complex designs and unknown degree of overlap. In this research, we developed four regression coefficient estimators in dual frame surveys. Simulation results show that all the proposed methods work...

The IEEE has recently released the 802.3bj standard that defines two different low power operating modes for high speed Energy Efficient Ethernet physical interfaces (PHYs) working at 40 and 100Gb/s. In this paper, we propose the use of the well-known frame coalescing algorithm to manage them and provide an analytical model to evaluate the influence of coalescing parameters and PHY characterist...

A dimension invariance property of finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation ...

Given a frame for a subspace W of a Hilbert space H , we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a gener...