- #1
MathOamtiX
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Homework Statement
Two receivers, d=5 [meters] apart, are recording an air wave signal.
The air wave travels in v=330 [m/sec] and coming from one side of the receivers.
The air wave contains all the frequencies between 10 [Hz] and 200 [Hz].
a) If we sum up the recorded signal from the two receivers, does all the energy from the original wave will be conserved ? explain.
b) The sampling rate in the receivers is Δt=0.004 [Sec], sketch the amplitude spectrum of the sum series.
Homework Equations
[itex]$\omega =2\pi f$[/itex] ,
[itex]\[\sum\limits_{n=0}^{N-1}{|}{{x}_{n}}{{|}^{2}}=\frac{1}{N}\sum\limits_{k=0}^{N-1}{|}{{X}_{k}}{{|}^{2}}\][/itex] (Parseval Theorem)
and maybe the DFT of sin/cos functions
The Attempt at a Solution
a) I know that the starting point should be the distance and the velocity.
so we get t=v/d and from that the frequency can be calculated somehow.
also the wave is a combination of known sin waves, so after DFT it transfers into a delta function.
b) Here i don't even know how start, since nothing is implied about the amplitude !