Optimal Sampling Rate for Spectrum Replication: Expert Homework Help

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The discussion centers on determining the optimal sampling rate for a signal with a specified spectrum to avoid aliasing and ensure proper spectrum replication. The signal's bandwidth is identified as 30 Hz, but there is confusion regarding the correct formula for calculating the Nyquist frequency in a passband spectrum. Participants note that the original spectrum ranges from 95 MHz to either 115 MHz or 125 MHz, which complicates the sampling rate determination. One participant suggests that the lowest sampling rate should be 35 MHz, but others express uncertainty about this conclusion based on the provided spectrum. The need for clarification on the problem statement is emphasized to resolve the discrepancies in calculations.
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Homework Statement


In some cases, the spectrum replication property of sampling can be used as a substitute for demodulation. Given a signal xa(t) with the spectrum shown, what is the lowest sampling rate that will ensure both no aliasing of the spectrum, and that one of the spectrum replicas is centered at f = 0?

Figure_zpsyaqlj2ks.png

http://s716.photobucket.com/user/Pitoraq/media/Figure_zpsyaqlj2ks.png.html?sort=3&o=0
(Note it should be 125 Hz to the right in the figure not 115 Hz)

Homework Equations



f(Nyquist fre.) = (1/2)*v(sampling freq.) (1)

The Attempt at a Solution



If the bandwidth is 125-95 = 30 Hz

How can i then determine the lowest sampling rate ?

The answer should be 35 MHz
 
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Hi Firben. What have you found from your google searches?
 
f(Nyquist fre.) = (1/2)*v(sampling freq.) [/quote]
This is not the correct formula for a passband spectrum. It would be if the original spectrum went from dc to 115 MHz (or 125 MHz) but it goes only from 95MHz to 115 or 125 MHz.
EDIT:
I can't resolve the correct answer (fs = 35 MHz) with any of a spectrum of 95 -115 MHz, or one of 85 -125 MHz, or one of 95 -125 MHz. I suggest you re-check the problem statement.
 
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