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In this paper, we give a new proof of the solution of the rational covari-ance extension problem, an interpolation problem with historical roots in potential theory, and with recent application in speech synthesis, spectral estimation, stochas-tic systems theory, and systems identification. The heart of this problem is to pa-rameterize, in useful systems… (More)

Ahstract-A band-limited signal of finite energy can be reconstructed from its samples taken at the Nyquist rate. Moreover, the reconstruction is stable, a feature crucial for implementation: a small error in the sample values generates ollly a correspondingly small error in the resulting signal. The Nyquist sample values are mutually independent, so that… (More)

- H J Landau, W L Miranker
- 2003

In this paper we devise a method for recovering band limited signals which have been subjected to a distorting procedure called companding. A band limited signal is a function in L2 whose Fourier transform vanishes outside of a bounded interval. In practice most real signals are in this class since they have no indefinitely high frequency components. The… (More)

- Lothar Reichel, Wg, W Gautschi, H J Landau, G V Milovanovi´c
- 2013

In a recent paper, D. Hajela and P. Seymour proved that for O~-bt~-b~ 1, ~t=(Iog~ 3)/2, b~b] +(1-b0"b~ +(1-ba)~(l-b~)'_~ 1, and drew from this inequality a variety of interesting results in combinatorial geometry. They also conjectured a generalization of the inequality to n variables, which they showed to imply a lower bound on the number of different… (More)

- Ahmed I Zayed, D Slepian, H Landau, H Pollak
- 2015

—The problem of maximizing the energy of a signal bandlimited to E1 = [−σ, σ] on an interval T1 = [−τ, τ ] in the time domain, which is called the energy concentration problem, was solved by a group of mathematicians, at Bell Labs in the 1960s. The goal of this article is to solve the energy concentration problem for the n-dimensional special affine Fourier… (More)

- Ahmed I Zayed, D Slepian, H Landau
- 2013

—An important problem in communication engineering is the energy concentration problem, that is the problem of finding a signal bandlimited to [−σ, σ] with maximum energy concentration in the interval [−τ, τ ], 0 < τ, in the time domain, or equivalently, finding a signal that is time limited to the interval [−τ, τ ] with maximum energy concentration in [−σ,… (More)