Optimal Sampling Rate for Spectrum Replication: Expert Homework Help

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SUMMARY

The discussion focuses on determining the optimal sampling rate for spectrum replication, specifically for a signal xa(t) with a bandwidth ranging from 95 MHz to 125 MHz. The correct lowest sampling rate to avoid aliasing and ensure one spectrum replica is centered at f = 0 is established as 35 MHz. The participants clarify that the Nyquist frequency formula used initially was incorrect for the given passband spectrum, emphasizing the need for accurate bandwidth assessment.

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  • Understanding of Nyquist Theorem and Nyquist frequency
  • Knowledge of passband spectrum characteristics
  • Familiarity with signal processing concepts
  • Experience with frequency domain analysis
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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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