Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums

Abbott, Derek; Davis, B.R.; Phillips, Nicholas J.; Eshraghian, Kamran

doi:10.1109/13.485226

Cited by 28 publications

(26 citation statements)

References 33 publications

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“…When Johnson showed the formula to his friend, Nyquist, it then took only a month to solve the problem of how to theoretically derive it. 10 The golden age of noise began and many talented workers contributed to the mathematical formalisms we use today such as Wiener, Levy, Ornstein and Uhlenbeck, Ito, and others. Let us now fast forward to the present.…”

Section: Introductionmentioning

confidence: 99%

Overview: Unsolved problems of noise and fluctuations

Abbott

2001

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Noise and fluctuations are at the seat of all physical phenomena. It is well known that, in linear systems, noise plays a destructive role. However, an emerging paradigm for nonlinear systems is that noise can play a constructive role-in some cases information transfer can be optimized at nonzero noise levels. Another use of noise is that its measured characteristics can tell us useful information about the system itself. Problems associated with fluctuations have been studied since 1826 and this Focus Issue brings together a collection of articles that highlight some of the emerging hot unsolved noise problems to point the way for future research. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1398543͔The study of fluctuations crosses many discipline boundaries as ''noise'' is a ubiquitous phenomenon. Noise is traditionally thought of as an unwanted effect that degrades the performance of a system. However, the emerging paradigm now recognizes that noise can play both a destructive or constructive role, depending on the circumstances. Thus there is now an intense interest in noise in many biological, physical, and other systems. The collection of papers in this Focus Issue examines open problems and debates surrounding the role of noise in both chaotic and nonchaotic systems. In this Overview we introduce the concepts of stochastic resonance, Brownian ratchets, 1Õf noise and vacuum fluctuations, and some problems surrounding them.

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Section: Introductionmentioning

confidence: 99%

Overview: Unsolved problems of noise and fluctuations

Abbott

2001

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In our studies, we used saline whose RF electrical characteristics approximate the average of those of biological tissue. 35 For intravascular applications 25,32 wherein the device is always in blood, the load is constant inasmuch as its thermal sensitivity is highly localized about the antenna junction.…”

Section: Discussionmentioning

confidence: 99%

“…1,32 Ordinarily, the bandwidth of the MRI receiver is much less than that afforded by the coil quality factor, Q, of tuned loaded MRI detectors, and the Q's of internal coils are even lower. Thus, over a small bandwidth (e.g., ±200 KHz at 128 MHz), the expected noise variance is essentially constant, with…”

Section: B Effect Of Sample Load and Impedance Matchingmentioning

confidence: 99%

Monitoring local heating around an interventional MRI antenna with RF radiometry

2015

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Purpose: Radiofrequency (RF) radiometry uses thermal noise detected by an antenna to measure the temperature of objects independent of medical imaging technologies such as magnetic resonance imaging (MRI). Here, an active interventional MRI antenna can be deployed as a RF radiometer to measure local heating, as a possible new method of monitoring device safety and thermal therapy. Methods: A 128 MHz radiometer receiver was fabricated to measure the RF noise voltage from an interventional 3 T MRI loopless antenna and calibrated for temperature in a uniformly heated bioanalogous gel phantom. Local heating (∆T) was induced using the antenna for RF transmission and measured by RF radiometry, fiber-optic thermal sensors, and MRI thermometry. The spatial thermal sensitivity of the antenna radiometer was numerically computed using a method-of-moment electric field analyses. The gel's thermal conductivity was measured by MRI thermometry, and the localized time-dependent ∆T distribution computed from the bioheat transfer equation and compared with radiometry measurements. A "H-factor" relating the 1 g-averaged ∆T to the radiometric temperature was introduced to estimate peak temperature rise in the antenna's sensitive region. Results: The loopless antenna radiometer linearly tracked temperature inside a thermally equilibrated phantom up to 73• C to within ±0.3 • C at a 2 Hz sample rate. Computed and MRI thermometric measures of peak ∆T agreed within 13%. The peak 1 g-average temperature was H = 1.36 ± 0.02 times higher than the radiometric temperature for any media with a thermal conductivity of 0.15-0.50 (W/m)/K, indicating that the radiometer can measure peak 1 g-averaged ∆T in physiologically relevant tissue within ±0.4• C. Conclusions: Active internal MRI detectors can serve as RF radiometers at the MRI frequency to provide accurate independent measures of local and peak temperature without the artifacts that can accompany MRI thermometry or the extra space needed to accommodate alternative thermal transducers. A RF radiometer could be integrated in a MRI scanner to permit "self-monitoring" for assuring device safety and/or monitoring delivery of thermal therapy. C 2015 American Association of Physicists in Medicine. [http://dx

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“…An interesting and instructive example of the alternate approach, the Fourier transform of a temporally windowed stochastic process, is the paper by Abbott et al, 27 whose spectral analysis of Johnson noise may serve as an introduction to a slightly more sophisticated technique to attack problems such as this.…”

Section: Fourier Seriesmentioning

confidence: 99%

A frequency-domain derivation of shot-noise

Rice

2016

American Journal of Physics

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A formula for shot-noise is derived in the frequency-domain. The derivation is complete and reasonably rigorous while being appropriate for undergraduate students; it models a sequence of random pulses using Fourier sine and cosine series, and requires some basic statistical concepts. The text here may serve as a pedagogic introduction to the spectral analysis of random processes and may prove useful to introduce students to the logic behind stochastic problems. The concepts of noise power spectral density and equivalent noise bandwidth are introduced.

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Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums

Cited by 28 publications

References 33 publications

Overview: Unsolved problems of noise and fluctuations

Overview: Unsolved problems of noise and fluctuations

Monitoring local heating around an interventional MRI antenna with RF radiometry

A frequency-domain derivation of shot-noise

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