2016
DOI: 10.1119/1.4934706
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A frequency-domain derivation of shot-noise

Abstract: 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… Show more

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Cited by 12 publications
(7 citation statements)
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“…When ⟨ n ⟩ is computed over long times, λ is a constant. However, as the observation or averaging time becomes shorter, the observed rate of formation will deviate from the mean due to random variations in the time interval between successive events, or equivalently, random variations in the number of events within the defined time interval . This behavior, which is illustrated in Figure , can be described by considering the variance in the observed event rate, n /τ, around the mean, given by …”
Section: Resultsmentioning
confidence: 99%
“…When ⟨ n ⟩ is computed over long times, λ is a constant. However, as the observation or averaging time becomes shorter, the observed rate of formation will deviate from the mean due to random variations in the time interval between successive events, or equivalently, random variations in the number of events within the defined time interval . This behavior, which is illustrated in Figure , can be described by considering the variance in the observed event rate, n /τ, around the mean, given by …”
Section: Resultsmentioning
confidence: 99%
“…4 (a) it is possible to determine the optimal working frequency range for the BHD as the interval between 1 MHz and 100 MHz approximately, where the difference INPSD has the typical white-noise flat trend and it is compatible with the expected ideal onesided Power Spectral Density (PSD) of the shot noise (dashed black line). This is defined as P SD shot−noise = 2eI, where e is the electron charge and I is the detector output current [57]. For high frequencies, above 100 MHz, the data drop below the ideal shot-noise level is due to the finite bandwidth of the setup (detector and oscilloscope).…”
Section: Resultsmentioning
confidence: 99%
“…The main source of noise in the optical detection system is photon shot noise. For low spin contrast 1, which is a good approximation for NV centers, the noise is Poissonian and white and the power spectral density is simply given by S = R 0 [37]. Assuming a signal integration time of t int , the equivalent noise bandwidth of the filter from Eq.…”
Section: Sensitivitymentioning
confidence: 99%