A sinusoidal signal of 600hz is sampled with 1khz, If the sampled signal is applied to an ideal low pass filter of 500 hz, what is the output?
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$\begingroup$ We appreciate it if you share your own ideas on a problem. Your question is just a copy of the exercise, but for us the question remains what is your question concerning this exercise? $\endgroup$– Matt L.Commented Dec 29, 2015 at 6:50
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2 Answers
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This is basic sample theory. when you want more of the background you can find this at wikipedia. Check also there pages about sampling and Nyquist The output frequency will be: $$ F_{out} = \frac{Fs}{2} - f_0 \text{ so } 500-600 = -100 $$ The result of this will me that you measure the signal at $400 Hz$
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thirI believe it is a nonsensical question, or at least a tricky, meant to detect students who have a shaky knowledge, and whose anwser deserves a lot of care.
First trick: if the $600$ Hz signal is sampled at $1000$ Hz, it will endure aliasing (a proper sampling frequency would be above $2 \times 600$ Hz). If the sampling process is perfect, it will appear as a sine at the mirror frequency $2*\frac{1000}{2}-600 = 400$ Hz.
The signal (that is assume real)) is now in the $[0,500] $ Hz band. An ideal-low pass cutting at $500$ Hz would thus be an all-pass, second trick, and would be utterly hard to design, numerically, in that case (third trick).
So in theory, the output signal would be the same (aliased) signal as the one from the first stage, fourth trick in a way.
answered Dec 28, 2015 at 12:17