VIII Evaluation, Design and Extrapolation Methods for Optical Signals, Based on Use of the Prolate Functions

Frieden, B. Roy

doi:10.1016/s0079-6638(08)70049-0

Cited by 144 publications

(99 citation statements)

References 29 publications

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“…Several researchers such as G. Toraldo Di Francia in [11], H. Osterberg and J. Wilkins in [12], J. Harris in [13] and C. Barnes in [14] have proposed various methodologies with different shortcomings, to overcome the diffraction problem in imaging systems. B. Frieden [8] proposed a theory which overcame the shortcomings of the methodologies proposed by these previous researchers. To solve the diffraction problem, Frieden used linear prolate functions to construct a point amplitude response whose side lobes do not increase in size even when the order 'n' of the prolate function is increased.…”

Section: Methodsmentioning

confidence: 99%

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Design and Simulation of a Linear Prolate Filter for a Baseband Receiver

Soman¹,

Čada²

2017

J Inform Tech Softw Eng

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Digital signals transmitted over a communication channel are mostly affected by noise. To reduce the detrimental effects of noise, a band-limited filter is used at the receiver, which results a phenomenon known as Inter-Symbol Interference. To avoid Inter-Symbol Interference, filters with greater bandwidth can be used. However, this causes high frequency noise to interfere with the transmitted information signal. This paper illustrates an innovative way to reduce Inter-Symbol Interference in the received baseband signal. This is achieved by making use of the processing bandwidth of a special filter designed by using Linear Prolate Functions. The result of the signal reconstruction capabilities of a prolate filter are compared with those of an ideal low pass filter in this paper.

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Section: Methodsmentioning

confidence: 99%

“…The properties of prolate functions were first studied by Slepian and Pollak in [5] and were analytically discussed in detail by Frieden in [8]. With regards to this paper, some of the important properties of linear prolate functions are as follows:…”

Section: Notations and Properties Of Linear Prolate Functionsmentioning

confidence: 99%

Design and Simulation of a Linear Prolate Filter for a Baseband Receiver

Soman¹,

Čada²

2017

J Inform Tech Softw Eng

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“…In order to improve the antenna characterization results as compared to a standard transformation by exploiting the a priori information on the shape and size of the source [8,9,21], the aperture field E a is represented by the Prolate Spheroidal Wave Functions (PSWFs) as [9,[21][22][23]]…”

Section: "Complex" Nfff Transformationmentioning

confidence: 99%

“…where Φ i [c w , w] is the i-th, 1D PSWF with "space-bandwidth product" c w [22,23], c x = au , c y = bv and u and v locate the spectral region of interest [21], as u ≤ β and v ≤ β. In Eq.…”

Section: "Complex" Nfff Transformationmentioning

confidence: 99%

Nufft-Accelerated Plane-Polar (Also Phaseless) Near-Field/Far-Field Transformation

Capozzoli¹,

Curcio²,

Liseno³

2012

PIER M

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Abstract-The paper introduces the use of Non-Uniform Fast Fourier Transform (NUFFT) routines in "complex" (i.e., amplitude and phase) and phaseless Near-Field/Far-Field transformations. The use of those routines results computationally very convenient when non-regular field sampling prevents the use of standard FFTs. The attention is focused on a plane-polar acquisition geometry. Numerical and experimental results show the effectiveness of the developed algorithms.

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“…The properties of the prolate spheroidal wave functions have been extensively treated in the literature. 13,14,15,16,17,18,19,20 The analysis of the inversion (superresolution) problem can be carried out using the properties of the prolate spheroidal wave functions without explicit use of the fact that the defining operator is compact, self-adjoint, etc. Since the prolate spheroidal wave functions are complete in the interval I , property 2), we can expand the input as…”

Section: The Ideal Sar Modelmentioning

confidence: 99%

Superresolution and Synthetic Aperture Radar

Dickey¹,

Romero²,

Doerry³

2001

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Superresolution concepts offer the potential of resolution beyond the classical limit. This great promise has not generally been realized. In this study we investigate the potential application of superresolution concepts to synthetic aperture radar. The analytical basis for superresolution theory is discussed. The application of the concept to synthetic aperture radar is investigated as an operator inversion problem. Generally, the operator inversion problem is ill posed. A criterion for judging superresolution processing of an image is presented.-4 - ACKNOWLEDGEMENTSThe authors would like to thank John M. DeLaurentis for extensive discussions on the underlying functional analysis and critique of the manuscript. We would like to thank

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VIII Evaluation, Design and Extrapolation Methods for Optical Signals, Based on Use of the Prolate Functions

Cited by 144 publications

References 29 publications

Design and Simulation of a Linear Prolate Filter for a Baseband Receiver

Design and Simulation of a Linear Prolate Filter for a Baseband Receiver

Nufft-Accelerated Plane-Polar (Also Phaseless) Near-Field/Far-Field Transformation

Superresolution and Synthetic Aperture Radar

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