Ah, and I think here's where I really went wrong: I keep failing to take into account that mathematically, when we are talking about frequencies in the signal, we are speaking about infinitely long sine waves - and in the examples that I imagine, I picture extremely finite, rather short sections...
I thought the perfect reconstruction predicted is only valid for an infinitely long sample time, and no one has that long.
You are right my language was unclear and I jumbled things I shouldn't have. I think I did mean that there is a timing uncertainty at 1/F_s, though. What do you mean by...
I think my argument is more that we can't claim perfect reconstruction, at any frequency north of DC. There will always be a time uncertainty of up to 1 / F_s at every frequency. This translates to a negligible phase uncertainty at lower frequencies, but I think it can create up to 90 degrees...
Although, I would point out that it wouldn't be right to call it theoretically perfect reconstruction... as frequencies approach the Nyquist frequency (Fs/2), there is no provision to take the phase into account.
Example: if you had a signal consisting of only the Nyquist frequency, and the...
You know the voltage across the resistor, good. So you know the voltage of the node above the 5Ohm resistor. Can you tell us how much current goes in and out of that node? Where does it come from? Where does it flow to?
And when answering these types of questions, we often have to be pedantic. So since there is no meaningful difference between "without loss" and "without ANY loss", I think that is the answer they're probably looking for.
And so, I think you can now apply the reasoning you originally used for...
I think I steered you wrong on that... it only helped me because it meant that I did the algebra over and did not repeat an algebraic mistake the first time.
But make no mistake that I do end up with a proper expression whose limit is C1/(C1+C2).
Also, your terms look funny - you should...
And as long as I'm not being rigorous, I feel I can wink and say it's not 0/0 or even 0/(0+0),
but it's more like almostzeroC1/(almostzeroC1+almostzeroC2). Factor out the almostzero and there you go. ;)
Or maybe I was just solving the problem that I ran into and didn't read closely about the problem you were having.
To answer your question, "How do I take the magnitude of this?", well, to find the magnitude of a complex term, you multiply the term by its complex conjugate and then take the...
OK, got it. ... How about you try to do it over, but this time, before you create your expression "A", try NOT multiplying top and bottom by R1 (or R2 for "B")
see if that works for you.