# Lowest Sampling rate

1. Aug 24, 2016

### Firben

1. The problem statement, all variables and given/known data
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?

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)

2. Relevant equations

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

3. 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

Last edited by a moderator: Aug 24, 2016
2. Aug 24, 2016

### Staff: Mentor

3. Aug 25, 2016

### rude man

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.

Last edited: Aug 27, 2016