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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: ...


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

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

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

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 ...


3

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 ...


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

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

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 ...


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 see from your picture that most of the surrounding of the pool is made of straight and rigid objects, these objects make more reflections of sounds than absorptions, also allow for easy transmission. You can do a little soundproofing of the system, you can fill it with soft stuff like old rugs or cushions. You can also line the trap door with egg ...


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

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

Yes, you are literally simulating the flow of heat through a material. The diffusion coefficient is basically just a local measure of thermal conductivity and heat capacity. Rather than convolving your image with a Gaussian kernel, you could use something like the Crank-Nicholson method and make some number of timesteps. You could also adjust $D$ to make it ...


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 different sources of noise, and many different contexts that noise occurs, and when one says there is, "no such thing as a perfect one-way valve", one needs to be more specific about the particular context one is referring to. If one uses a one way valve where the input is a high pressure system, and the valve is isolating the high pressure from ...


1

10 decibels means ten times the power density of sound. That is chosen so that ten decibels equals one bel, and a one bel increase simply adds a zero on the end of the sound power density. Twenty decibels multiplies by 10 twice, so twenty decibels is an overall 100-fold increase in the sound. That means one decibel multiplies the sound by the smaller ...


1

For pink noise, the power spectrum falls off as 1/f. Remember that power is amplitude squared. For an electrical signal, power is voltage across times current flowing through a load, and the current follows from Ohm's Law. It is possible to arrange resistors and capacitors as a low pass filter to make an approximation of pink noise, but it's not precise. ...


1

Mechanical friction is a perfectly fine example. The coefficient of friction between two materials does not approach zero at absolute zero. Electrical resistance (as pointed out by Alexander) is another example. Some materials (superconductors) have zero resistance at absolute zero, but by no means all of them! I would say that $\gamma \neq 0$ while $T=0$ ...


1

The way I would approach this is to consider blackbody radiation, where a spherical blackbody radiator is isotropic, e.g. it emits radiation equally in all directions. If we were to model the noise introduced by such a blackbody, it would be additive Gaussian white noise. In this example, it is called white noise because it has a flat power spectrum ...


1

The noise may have no preferred direction, but for large enough volumes the average $$\langle\mathbf{F}\rangle_V=\frac{1}{V}\int_V \mathbf{F}(x) d^3x$$ will approach the constant term. Thus the field is not isotropic and there is a preferred direction: that of averages over sufficiently large volumes. (Here, of course, specifying the direction to arbitrary ...


1

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 ...


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 ...


1

From your description of the experiment (please correct me if my assumptions are wrong), it sounds like your apparatus consists of the application of a controlled stress to the sample (and the sensor), and the resulting strain in the sensor is measured. Whenever the stress applied by your apparatus changes, it will take some time for the system to settle to ...



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