Prosthaphaeresis revisited

Thoren, Victor E.

doi:10.1016/0315-0860(88)90047-x

Cited by 16 publications

(5 citation statements)

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“…The UWB radar emits a sinusoidal signal (the carrier signal) with a frequency f U represented by

A false(t false) = X \cos false(2 π f_{U} t false)

The motor vibrates with a specific characteristic frequency f MS (modulating signal) represented by

B false(t false) = Y \cos false(2 π f_{MS} t false)

As per the characteristic of microwave signals, amplitude modulated by a mechanically oscillating object in the signal path between a transmitter and receiver [14], so, the A ( t ) is amplitude modulated with B ( t ) and the resultant signal is given by

\begin{matrix} right leftthickmathspace.5em \\ C (t) & = {(][, 1 + B false(t false))}^{*} A (t) \\ = A (t) + A (t)^{*} B (t) \end{matrix}

By using prosthaphaeresis identities [15, 16], C ( t ) can be shown to be the sum of three sine waves, given by

C false(t false) = X \cos false(2 π f_{U} t false) + \frac{X Y}{2} [\begin{matrix} \cos 2 π (f_{U} + f_{normalMS}) t + \\ \cos 2 π (f_{U} - f_{normalMS}) t \end{matrix}]

Therefore, the modulated signal has three components, i.e. the high‐frequency carrier wave A ( t ) and two pure sine waves (sidebands) with frequencies slightly above and below the carrier frequency.…”

Section: Framework Of the Proposed Methodsmentioning

confidence: 99%

Non‐invasive method for rotor bar fault diagnosis in three‐phase squirrel cage induction motor with advanced signal processing technique

Barusu¹,

Sethurajan²,

Meganathan

2019

J. eng.

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“…The UWB radar emits a sinusoidal signal (the carrier signal) with a frequency f U represented by

A false(t false) = X \cos false(2 π f_{U} t false)

The motor vibrates with a specific characteristic frequency f MS (modulating signal) represented by

B false(t false) = Y \cos false(2 π f_{MS} t false)

\begin{matrix} right leftthickmathspace.5em \\ C (t) & = {(][, 1 + B false(t false))}^{*} A (t) \\ = A (t) + A (t)^{*} B (t) \end{matrix}

By using prosthaphaeresis identities [15, 16], C ( t ) can be shown to be the sum of three sine waves, given by

C false(t false) = X \cos false(2 π f_{U} t false) + \frac{X Y}{2} [\begin{matrix} \cos 2 π (f_{U} + f_{normalMS}) t + \\ \cos 2 π (f_{U} - f_{normalMS}) t \end{matrix}]

Section: Framework Of the Proposed Methodsmentioning

confidence: 99%

Non‐invasive method for rotor bar fault diagnosis in three‐phase squirrel cage induction motor with advanced signal processing technique

Barusu¹,

Sethurajan²,

Meganathan

2019

J. eng.

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“…Using prosthaphaeresis identities [38,39], Z t shows the sum of three sine wave Z t = Acos 2π f UWB t…”

Section: Handheld Doppler Uwb Radar Signal Acquisitionmentioning

confidence: 99%

“…The UWB radar emits a sinusoidal signal (consider carrier signal) with a frequency

f_{UWB}

represented as

X false(t false) = A \cos ()(, 2 π f_{UWB} t)

The motor vibrates with a specific characteristic frequency

f_{normalM}

(modulating signal) represented as

Y ()(, t) = B \cos ()(, 2 π f_{normalM} t)

As per the characteristic of microwave signal, amplitude modulated by a mechanically oscillating object in the signal path between a transmitter and receiver [17], therefore, the

X ()(, t)

is amplitude modulated with

Y ()(, t)

and resultant signal is

\begin{matrix} right leftthickmathspace.5em \\ Z (t) & = [1 + Y (t)] \times X (t) \\ = X (t) + X (t) \times Y (t) \end{matrix}

Using prosthaphaeresis identities [38, 39],

Z ()(, t)

shows the sum of three sine wave

\begin{matrix} right leftthickmathspace.5em \\ Z (t) = & A \cos (2 π f_{UWB} t) \\ + \frac{A B}{2} ([, \cos 2 π ()(, f_{UWB} + f_{normalM}) t) (], + \cos 2 π ()(, f_{UWB} - f_{normalM}) t) \end{matrix}

Therefore, the modulated signal has three components such as the carrier wave

X

…”

Section: Handheld Doppler Uwb Radar Signal Acquisitionmentioning

confidence: 99%

Low‐cost SPLL‐based electrical faults identification for three‐phase squirrel cage induction motor using handheld Doppler radar signal analysis

Barusu

Sethurajan

Meganathan

2018

IET Power Electronics

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The condition monitoring of an induction motor performs by contact or non-contact methods. The contact methods execute via vibration signal, temperature measurement, current signature analysis and so on, and the non-contact methods accomplish via thermal imaging, temperature measurement and acoustic emission measurement. The contact method requires human expertise to evaluate failures and it is laborious. The authors propose a novel, low-cost and non-contact method using software phase locked loop (SPLL) for electrical fault identification in the three-phase squirrel cage induction motor. The handheld Doppler ultra wideband radar transmitted signal is focused on the induction motor and the reflected signal is analysed with SPLL. The SPLL error signal correlates the faults. From the experimental results, the fault identification of motor in the earlier stage achieves better accuracy of the different motor fault condition. The pattern of error signal provides the information of various faults in squirrel cage induction motor.

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“…The foremost major advocate for scientific computation using mechanical calculating machines in the early twentieth century, Leslie Comrie, argued that careful examination of the errors in tables strongly indicated that most of these new sets of them simply were taken, usually with no attribution, from sixteenth-and seventeenth-century tables. 4 The upsurge of mathematical astronomy in early modern Europe, most associated with Nicolas Copernicus, Tycho Brahe, and Johannes Kepler, spurred the development of new methods for performing laborious calculations, particularly techniques for abridging multiplication by some sort of reduction to addition (Thoren 1988). While the first widespread techniques involved trigonometric identities, John Napier devised the more straightforward technique of logarithms early in the seventeenth century.…”

Section: Calculation "By Hand"mentioning

confidence: 99%

Calculating Devices and Computers

Jones¹

2016

A Companion to the History of Science

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Focusing upon computation, storage, and infrastructures for data from the early modern European period forward, this chapter stresses that the constraints of computing technologies, as well as their possibilities, are essential for the path of computational sciences. Mathematical tables and simple contrivances aided calculation well into the middle of the twentieth century. Digital machines replaced them slowly: adopting electronic digital computers for scientific work demanded creative responses to the limits of technologies of computation, storage, and communication. Transforming the evidence of existing scientific domains into data computable and storable in electronic form challenged ontology and practice alike. The ideational history of computing should pay close attention to its materiality and social forms, and the materialist history of computing must pay attention to its algorithmic ingenuity in the face of material constraints.

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Prosthaphaeresis revisited

Cited by 16 publications

References 0 publications

Non‐invasive method for rotor bar fault diagnosis in three‐phase squirrel cage induction motor with advanced signal processing technique

Non‐invasive method for rotor bar fault diagnosis in three‐phase squirrel cage induction motor with advanced signal processing technique

Low‐cost SPLL‐based electrical faults identification for three‐phase squirrel cage induction motor using handheld Doppler radar signal analysis

Calculating Devices and Computers

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