Extremely late to the party here:
Consider a circuit with two oppositely polarized sinusoidal sources (identical amplitude and frequency and 180 degrees out of phase). Put an ideal capacitor in the circuit. If you want, let the one source be cos(omegat) and the other source be cos(omegat)*u(t) (turns on at t = 0).
There is no power dissipation in this idealized circuit. There is conservation of energy. Both sources put energy into the circuit and when both sources are on, there is no energy being stored in the capacitor - which means that the sources are absorbing power.
Consider a string being excited by two sources (again a perfect string with no friction and therefore no heat dissipation). The oscillations cause destructive interference. Where did the energy go?
Consider a lossless transmission line or a waveguide with sources at either end causing destructive interference.
From what I have read so far, it appears that in all these cases the sources themselves absorb (or possibly reflect) energy. The point is that for all the places where you have destructive interference, there are places where there is constructive interference in such a way that the total energy is conserved.
So, I think we can say that total destructive interference in an entire system (where the system is defined as that region that contains all the sources) is impossible. The total power “lost” by the destructive interefence will show up somehwere else in the form of constructive interference.
So, in my case, I have aliases of noise showing up in my band of interest (because I didn’t apply an appropriate anti-aliasing LPF before taking measurements!). Lets say we are only interested in 100 Hz. We have the real response of the system at 100 Hz and we have an alias of noise from 4900 Hz (the sampling rate was 5000 samples per second, so the Nyquist frequency is 2500 Hz). The “sources” here are the plethora of forces acting on the train to cause 100 Hz vibration and that cause the 4900 Hz noise. So, the total system is comprised of the train plus the various other things (tracks, motors, etc) that cause train vibration. If we are only looking at 100 Hz, we see the superposition of the train response and the alias of the noise at 4900 Hz. If the alias is causing destructive interference, then I think it would be right to say that the oscillations at this frequency are adding up somewhere else in the system (on the train at a different location from the accelerometer, in the tracks, etc).
See, it has been claimed that the aliases of the higher frequency noise would only cause the perceived acceleration spectral density to increase - and only occasionally would the perceived acceleration spectral density decrease as a result of aliasing. I’m trying to determine whether or not the aliases of the higher frequency noise would always add to the acceleration spectral density. Can the acceleration spectral density actually appear to be less as a result of the aliases? If so, what is the probability that this would occur? It seems to me that if the aliases actually can cause the perceived spectral density to decrease, then it would do so with a fairly high probability - assuming that the phase difference between the actual acceleration and the alias is random.
Some links about this. Some of the responses in these forums are really poor, but some I think are good. People keep trying to say “heat” or “dissipation.” But the conservation of energy principle still applies even in idealized lossless systems, so anyone who brings up power dissipation is missing the point.
http://cr4.globalspec.com/thread/54954
On a separate point, I’m a bit confused about the nature of accelerometers. Accelerometers (according to my understanding) are sensors which convert acceleration to voltage (or possibly to currrent). If the accelerometer is ideal, then the relationship between the acceleration and the voltage is linear. But a^2 has units of m^2/s^4 or W/(kgs). And V^2 has units of W/ohm. I’m not bothered by the kg and ohm differences; those are just constants of proportionality. I’m bothered by the W/s versus W difference. If a is proportional to v, then a = kV, where k has units of (m/s^2)/(V). But I would think in an ideal accelerometer, the energy into the accelerometer equals the energy out of the accelerometer. That is, the accelerometer converts mechanical power to electrical power without any power being dissipated. But mechanical power is Pmech = Fv = or ma*v. But the accelerometer isn’t measuring acceleration and speed, but only acceleration. So, then the acceleration spectral density I mentioned above is NOT a power spectral density, but a time-derivative of power spectral density. I just don’t have my mind really wrapped around this yet. It just seems to me that when a is proportional to V that there would probably be an energy loss somewhere - even in an “idealized” accelerometer. And I’m also noting that when I consider the acceleration spectral density, I don’t think I can assume that acceleration squared is conserved - even though power is always conserved.