Fourier Frames
نویسندگان
چکیده
منابع مشابه
On Fourier Frames
We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges’ theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a cla...
متن کاملDetecting Edges from Non-uniform Fourier Data Using Fourier Frames
Edge detection plays an important role in identifying regions of interest in an underlying signal or image. In some applications, such as magnetic resonance imaging (MRI) or synthetic aperture radar (SAR), data are sampled in the Fourier domain. Many algorithms have been developed to efficiently extract edges of images when uniform Fourier data are acquired. However, in cases where the data are...
متن کاملGeneralized Fourier Frames in Terms of Balayage
Based on Beurling’s theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient complexity to warrant new examples generally, and to resurrect the formulation of balayage in terms of covering criteria with an eye towards an expanded theory as w...
متن کاملOn Characterizations of Fourier Frames and Tilings
for all f ∈ H.A and B are called frame bounds.The sequence is called a tight frame if A = B. The sequence is called Bessel if the second inequality above holds. In this case, B is called the Bessel bound. Frames were first introduced by Duffin and Schaeffer [1] in the context of nonharmonic Fourier series, and today they have applications in a wide range of areas. A frame can be considered as a...
متن کاملSigma Delta quantization with Harmonic frames and partial Fourier ensembles
It is well known that a discrete band-limited signal can be made broad-banded if we randomly permute its entries. In this paper, we study the efficacy of such spectral whitening procedure and its application to Sigma Delta quantization in Compressed Sensing. As a side result, we show that a similar whitening phenomenon can be observed in a broad class of non-Fourier orthogonal transformations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2002
ISSN: 0003-486X
DOI: 10.2307/3062132