http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10487 This paper extends work of Shen and Walter and others concerning relationships between sampling and time-frequency localization. We consider approximate projections onto eigenspaces of time- and bandlimiting operators, expressed in terms of samples of bandlimited functions. We establish error estimates of eigenfunction samples and on matrices that can be used to generate approximations of these samples. Numerical comparisons are made between approximations generated by a method proposed by Walter, Shen and Soleski and an alternative method proposed by Karoui and Moumni. 2012-03-21T02:50:04.755Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:8144 One of the major differences between Paley-Wiener spaces of bandlimited signals and the principal shift-invariant (PSI) spaces of wavelet theory is that the latter, although shift-invariant, are in general not translation-invariant. In this paper we study the extra difficulties non-translation-invariance creates for the sampling theory of PSI and multiresolution spaces. In particular it is shown that sampling in PSI spaces requires an extra initialization step to determine the times at which sampled data is acquired. An algorithm is developed to provide this initialization and its effectiveness shown theoretically and demonstrated on a synthetic data set. 2011-07-07T01:50:12.763Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:6746 This chapter develops aspects of previous work that pertain distinctly to band-limited functions. In particular, we discuss some representation formulas for band-limited functions in terms of periodic nonuniform samples. In the case of multiband signals, periodic nonuniform sampling is often valid at a lower sampling rate than is uniform sampling, as will be discussed. Finally, we will consider some related questions about optimally time- and multiband-limited signals. 2010-09-19T23:40:02.879Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:5884 Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of developments in time-frequency and time-scale analysis are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. 2010-08-10T22:33:28.942Z ]]>