A definition of average time delay for a linear system

Simpson, R.; Houts, R. C.

doi:10.1109/proc.1967.5965

Cited by 7 publications

(3 citation statements)

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“…By the Schwarz inequality, we see from this that 0 ≤ C(τ) ≤ 1 and therefore 0 ≤ FF ≤ 1 and 0 ≤ D ≤ 1. In the special case of an allpass network (where |H(ω) | ≡ 1 for all ω), we can see from (14) and (15) that C(τ) = m 0 (τ) , so that m 0 (τ 0 ) = ± FF for such networks. Since f, g and h are all real functions of time, all integrals over frequency can be expressed as integrals over nonnegative frequencies only, and we have…”

Section: Distortion and The Fidelity Factormentioning

confidence: 99%

“…In this paper, we review a widely used measure of distortion called the fidelity or fidelity factor [4] widely used to characterise how well a system preserves the shape of a transmitted pulse, examining its behaviour in several simple cases to gain a sense of how well it performs this function. Essentially equivalent measures of distortion have been proposed, in some cases quite long ago, for analogue television, automatic control and other applications [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. If the signal bandwidth is not too large, we derive a simple analytical approximation for the fidelity factor that can be used to quickly assess the extent to which pulsed signals are degraded when passed through an LTI system, which could facilitate the design of a compensation network to alleviate the problem for a given system.…”

Section: Introductionmentioning

confidence: 99%

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Characterisation of distortion of narrowband signals by linear time‐invariant systems

Direen

Kuester

Elmansouri

2017

IET Microwaves, Antennas & Propagation

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The fidelity factor is a commonly used measure of the level of distortion of pulses in ultrawideband systems. In this study, a detailed examination is made of this quantity and how it relates to actual situations of signals transmitted through a linear time‐invariant system. Several examples are considered where the fidelity factor can be evaluated in closed form, or nearly so. In addition, a closed‐form analytical approximation is derived for the fidelity factor in the case where the bandwidth of the input signal is not too large. A number of examples are presented to illustrate the conditions under which this approximation can be expected to be accurate. The error of the approximation is found to be small unless the transfer function of the linear system varies rapidly near the centre frequency of the signal.

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Section: Distortion and The Fidelity Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterisation of distortion of narrowband signals by linear time‐invariant systems

Direen

Kuester

Elmansouri

2017

IET Microwaves, Antennas & Propagation

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“…Perhaps the most surprising point was his conclusion that P' --P -•-f(dP/di) is not true for backscatter. This equation is fundamental in linear system theory, being exactly equivalent to the more common form: delay ß --dO/do, (see, for example, Simpson and Hours [1967]).…”

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confidence: 99%

Discussion of paper by V. Agy, ‘Doppler shifts on high-frequency ground backscatter’

Croft¹

1969

J. Geophys. Res.

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Sky‐wave backscatter: A means for observing our environment at great distances

Croft¹

1972

Reviews of Geophysics

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For 45 years, men have measured and studied echoes from the distant surface of the earth, obtained with high-frequency signals (3 to 30 MHz) that travel to and from the scatterers via ionospheric refraction. During the last five years, much progress has been made in the understanding of this 'sky-wave backscatter.' An explanation of the various interacting phenomena is presented, as is a review of the current state of knowledge reflecting recent advances in observational methods and analytic techniques. New narrow-beam antennas, coupled with signal modulations that permit fine resolution in time delay, are beginning to yield information concerning the character of the scatterers, which now can be separately discerned. These narrow beams also permit study of polarization fading from small regions, and this shows promise as a means for learning the distant sea state. Doppler shifts of a fraction of a hertz on signals of tens of megahertz are separable, permitting isolation of sea returns from ground returns by virtue of the Doppler effect resulting from sea-wave speed; this a!so suggests a potential sea-monitoring principle. New modulation equipment permi,•s short-wave broadcast stations to make sky-wave backscatter soundings with exis'Ang transmitters as an adjunct to normal operations, so that area coverage can be observed in real time. Despite these advances, there is little practical app!ication of sky-wave backscatter as a means of environmental monitoring. This lack is attributed to the large remaining gaps in our understanding of the echoes and our inability to interpret the forms of data that can be acquired with equipment of reasonable cost. It is still not possible to calculate ionospheric structure from an observation of sky-wave backscatter although it is the opinion of many workers that this should be feasible. It is now at least. possible to carry out the reverse process, calculating sky-wave backscatter from an assumed ionosphere of much complexity. Study of such synthetic data is yielding additional insight into the causes of diverse forms of observed sky-wave backscatter. CONTENTS

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A definition of average time delay for a linear system

Cited by 7 publications

References 1 publication

Characterisation of distortion of narrowband signals by linear time‐invariant systems

Characterisation of distortion of narrowband signals by linear time‐invariant systems

Discussion of paper by V. Agy, ‘Doppler shifts on high-frequency ground backscatter’

Sky‐wave backscatter: A means for observing our environment at great distances

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