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7

The key to this is the physical principle that the quantity you're asking about (delay between noise and noise cancelling) carries dimensional information (i.e. it's a time) and therefore it has to depend on the specific situation. The simplest case is trying to cancel out a pure note, with a sinusoidal waveform, then the delay can be as long as you want: ...


7

The position of the mass, as a function of time, will simply be a filtered version of the random noise 'input' signal. To see this in the frequency domain, take the (magnitude of the) Fourier transform of both sides and rearrange: $$|X(\omega)| = \frac{1}{\sqrt{\left(1 - \omega^2\right)^2 + \frac{1}{Q^2}\omega^2}}|N(\omega)|$$ For $\omega = 1$, we have ...


6

There are a couple of main sources of intrinsic error (that is, not associated with counting photons from your source) which CCD's have. The first is as you have already mentioned called read noise. Here is a reasonable definition of read noise (taken from Romanishin's free pdf on Photometry): After an integration (exposure), the CCD must be read out to ...


5

I think you've just derived the Stefan-Boltzman law for a one-dimensional system. The T^4 comes from three dimensions. The more dimensions the quanta can populate the higher power of T you get.


5

Treating the signals as time series: If the first signal $S_1$ has a noise component $N_1$ added to it, then the noisy signal is $S_1+N_1$, similarly the second signal is $S_2+N_2$, so the difference signal would be $(S_1+N_1)-(S_2+N_2)$ and its signal to noise ratio would be $\langle(S_1-S_2)^2\rangle\over\langle(N_1-N_2)^2\rangle$ If the signals are ...


5

The threshold theorem says that if the error rate is below the threshold, a quantum algorithm with T locations (breadth times depth) can be made fault-tolerant with a blow-up (in both number of qubits and circuit size) by a factor which is a polynomial in the log of T. This is not enough to change BQP.


4

Apart from motor and bearing noise, most of the acoustic power comes from the eddy swirls following the trailing edge of the blade after it passes by. There is also an outward pulse of air as the leading edge of each blade pushes forward cutting the air. The trailing eddies produce a broad spectrum of random noise, modulated by the fan blade frequency. ...


4

It seems that the confusion is due to some unfortunate notation. As the OP states, Fano noise is due to the variance in photoelectron production per incident photon, and this should indeed be signal-dependent. However, the author also states that the total noise is given by: $$\tag{1} \sigma^2_\mathrm{TOTAL} = \sigma^2_\mathrm{READ} + \eta_i F_F + \eta_i S ...


4

I didn't see the episode, but it may be referring to "Phreaking", by which the signals from a CRT monitor can be listened-in on (it uses high frequency changing currents to display the information, so these will inevitably result in some RF radiation from which this information can in principle be extracted). Wikipedia article has a bit more info.


4

The idea that frequency modulated signals are more resilient to noise than amplitude-modulated ones is somewhat of a myth. Both are susceptible to noise: the demodulation sequence (including the human hearing and sight senses) reacts slightly differently to the effects of noise so that. It can be shown that if there is additive Gaussian noise with ...


4

The spectral density, or spectral function, describes the coupling between a small quantum system that is coupled to a larger environment. In many cases, this environment can be modelled effectively as a system of free bosonic or fermionic modes, with Hamiltonian (working in units with $\hbar = 1$) $$ H_B = \sum_k \omega_k b_k^{\dagger}b_k. $$ The mode ...


3

I don't think you really need an answer. The answer is yes and moreover what you have done is a pretty sound model of the effect of noise on the damped oscillator. I'm assuming that you have normalised frequencies so that the oscillator's natural frequency $\omega_n$ is one unit. The only factor you haven't mentioned and which you seem to have overlooked is ...


3

First, dB means nothing by itself. You need to give a reference level, like dBW or dB SPL. We'll assume dB SPL. Second, noise measurements from a point source like this require a distance measurement to be meaningful, since the level drops off with distance. We'll assume you're measuring at the same distance in both cases, and the fans are equidistant ...


2

Mechanical noise is a form of energy loss, which ultimately also will end as heat: the acoustic waves will be absorbed by different kinds of substances which will vibrate more causing friction which will ultimately cause a temperature rise. Note that the acoustic power is often extremely low, often no more than a few mW, and when those get absorbed by a ...


2

In statistical mechanics and thermodynamics you are describing systems with an extremely large number of possible variables or degrees of freedom, so describing EXACTLY what happens becomes impossible. Instead, you describe the average. To do this, you consider all physically possible configurations of your system, and say they are all equally probable. ...


2

I'm no ANC expert but I'm pretty sure the limit you're talking about would have something to do with the Haas effect (also called precedence effect). from Everest's Master Handbook of Acoustics: "...Haas found that in the 5 to 35 msec delay range the sound from the delayed loudspeaker has to be increased more than 10dB over the direct before it ...


2

I suppose you could say this is cheating, but you could surround the object emitting the sound with a perfect vacuum. Sound waves are vibrations in a medium; because a perfect vacuum has nothing in it, it cannot "conduct" (for lack of a better word) sound waves. You could attempt to levitate the object with magnets; because of Earnshaw's theorem, the setup ...


2

Definitions Define $W(2|1)$ as the transition probability per unit time from $1$ to $2$. This gets us the Master equation $$\partial_t p(a, m) = \int\!\!\!\!\int\! \left(W(a,m|a',m')p(a',m') - W(a',m'|a,m)p(a,m)\right)\mathrm{d}a'\mathrm{d}m'$$ Define further, for fun, $\mathbb{W}(a,m|a',m') = W(a,m|a',m') - \delta(a-a')\delta(m-m')\int\!\!\int ...


2

The heat equation comes from two very intuitive ideas: the rate of heat flow is proportional to the temperature difference, and the conservation of energy. First, from Newton's law of cooling or Fourier's law we get that the flow of heat is proportional to the gradient of the temperature: $$\mathbf{j}_{\text{heat}}=-k \nabla T$$ where $k$ is the thermal ...


1

The answer must be yes, because a force is applied then there will be some motion (if there was no motion then Newton's laws would be violated of course). The applitude will most likely be tiny and the damping term will ensure that it remains tiny. If there was no damping term you could get strong oscillation. The shape of the graph will most likely be ...


1

$\newcommand{\bra}[1]{\langle #1 |}$ $\newcommand{\ket}[1]{| #1 \rangle}$ $\newcommand{\braket}[2]{\langle #1 | #2 \rangle}$ $\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle}$ Although the question asks specifically about a harmonic oscillator, we can understand the meaning of the spectral density by considering a somewhat more general problem. ...


1

Are there any experimental results where the spectral noise density of shot noise is measured? Absolutely, yes. Here are just a few experiments measuring co-called "quantum shot noise": R.J. Schoelkopf, P.J. Burke, A.A.Kozhevnikov, D.E. Prober, and M.J. Rooks, Physical Review Letters, Vol 78, No. 17, p. 3370, April 1997. A. A. Kozhevnikov, R. J. ...


1

I think that, as any other Fourier transform, this is telling you which natural frequencies occur in the correlation function, and with which "weight". In the case of a harmonic oscillator you have only one characteristic frequency, namely $\omega_0^2$ (I believe the sign is just the possibility of oscillating with $\omega_0$ or in the opposite orientation ...


1

Letting $\mathbf{F}$ and $\mathbf{F}^{-1}$ be the forward and inverse discrete Fourier transform, the cyclic autocorrelation of a signal $A$ is given by $$S(A)=\mathbf{F}^{-1}\left[\mathbf{F}(A)\mathbf{F}(A)^*\right].$$ Let the low-passed signal $A_L$ be $$A_L=\mathbf{F}^{-1}\left[\mathbf{F}(A)\mathbf{F}(L)\right]$$ where $L$ is the low-pass filter in the ...


1

I do have the book, but not in front of me, so I am guessing from the form of equations. A Brownian particle can be represented by the stochastic differential equation $$m\dot{v} = -\xi v +\varepsilon$$ where the last term is the stochastic term, which is assumed to behave like $\langle\varepsilon\rangle = 0$, $\langle\varepsilon(t)\varepsilon(t')\rangle = ...


1

is white noise gaussian distributed ? Do you mean if the amplitude is gaussian distributed? Not necesarily. If it is, then it is properly called gaussian white noise. In the frequency/Fourier spectrum, how does white noise look like ? Ideally, over an infinite time interval, it will look as a flat line, because, by definition, it has the same ...


1

"a circuit that has different resistors at extremely different temperatures" -- Each resistor independently puts out its own noise related to its own temperature. "one long resistive element that has a temperature gradient across the whole thing" -- That's actually the same thing again. Treat it as a large number N of resistors in series, each with ...


1

Pink noise is not going to sound like voices; it sounds a lot more like water splashing in a fountain. The high frequencies are small, and it will not just sound like a garbled version of your voice. The reason is that the amplitude distribution you find in your voice cannot be maintained--voice doesn't have a 1/f distribution. You can maintain the phase ...


1

Bass consists of lower frequency ranges and longer wavelengths, meaning that produces those vibrations essentially over a longer distance, or at least with more "strength" so that the vibrations of the sound can travel through the plastic material. However since treble is of a higher frequency range, it travels shorter distances. This also means it cannot ...


1

There are many possible examples of this, and you may need to be more specific in what you want. Here are two that immediately come to mind: 1) A bead in a harmonic trap (or a bending cantilever) that is undergoing thermal kicks from Brownian motion. The strength of these fluctuations depends on temperature; if the temperature of the system changes over ...



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