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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

The situation you are describing is an example of Fresnel diffraction (or near-field diffraction). In general, when a wave propagates every point of the wave front can be thought of as its own source of waves traveling in all directions (called Huygens construction). It turns out that neighboring point sources along an infinite straight wave front reinforce ...


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

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

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

There are several ways I can interpret the question, so my main focus is going to be on the autocorrelation of an Ornstein-Uhlenbeck (O-U) process. So what is an O-U process and how is it different from regular Brownian diffusion? Brownian diffusion The stochastic differential equation (SDE) for Brownian diffusion of a particle can be written as ...


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

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 ...


2

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 ...


2

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 = ...


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

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

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

OK, a little bit like zephyr's answer, I started with white noise, took the FFT, and then scaled each frequency component up or down according to the square-root of the power at that frequency, then did inverse-FFT to get the time-domain signal. An equivalent approach would have been to generate the FFT directly by giving each component the appropriate ...


2

The terms "white noise" and "pink noise" are applied to noise that depends on a parameter. The equation you gave technically isn't noise at all--- it's a real number uniformly distributed between -1 and 1. But I will assume that you are calling the RAND function inside a routine, and that this routine is simulating some system in time, and every time step it ...


2

$\newcommand{\bra}[1]{\langle #1 |}$ $\newcommand{\ket}[1]{| #1 \rangle}$ $\newcommand{\braket}[2]{\langle #1 | #2 \rangle}$ $\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle}$ 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. ...


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

A single measurement like this has a lot of noise on it - and random signal is always going to have some random correlation. You should definitely not pay too much attention to the stuff that is in the tail of the correlation distribution - it's all noise. The fact that the built in function does not produce negative values is related to you only looking at ...


2

Zero mean so that the noise does not present a net disturbance to the system. There's as much positive noise as negative, so they cancel out in the long run. If the mean were not zero, then the noise would appear as an additional dynamic. For example, if the quantity were a force with some random jitter to it, then if the jitter did not have zero mean, ...


1

You will benefit by finding some tutorials on wave theory. In brief, assuming a spherical wavefront from the emitter, you are correct there's no direct path to the receiver. However, the edge of yourabsorber there causes diffraction (Huygen's principle), so thatsome of the sound wave (energy) will make its way to the receiver. You can see a demo of this, ...


1

The wikipedia page on Shot noise, probably answer your question: It is known that in a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after a great many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads ...



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