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I have a signal uniquely composed of a finite summation of standing wave sinusoids (well there's some DC and other background, but let's ignore those). Let's say I sample at some rate NT, and that my highest frequency is NT/2 (so I'm good on Nyquist). However, let's also say that I can only watch this signal for some time [itex]\tau[/itex], so I'm really only detecting [itex]\tau=NTp[/itex] (where p is number of samples) time overall.

So let's actually ignore the discrete time samples for a second, in continuous time I would see

[tex]g(t)=\sum_{N=1}^p \cos(\frac{2\pi \nu t}{N})[/tex]

So on one hand, how much time do I have to sample for to pick out all the correct frequencies. But, additionally, given that I am actually only measuring steps of NT seconds (sample and hold) does this affect the consequences of having a finite time window to measure all these beats correctly. Spectral leakage is pretty close to what I'm looking for, but not quite.