Optimal Sampling Rate for Spectrum Replication: Expert Homework Help

In summary, the conversation discusses the use of spectrum replication property of sampling as a substitute for demodulation in certain cases. The question asks for the lowest sampling rate that will prevent aliasing of the spectrum and ensure that one of the spectrum replicas is centered at f = 0. The given equation (1/2)*v(sampling freq.) is not the correct formula for a passband spectrum and the correct answer is 35 MHz, but it does not match with any of the given spectra. Further clarification is needed to determine the correct sampling rate.
  • #1
Firben
145
0

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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  • #2
Hi Firben. What have you found from your google searches?
 
  • #3
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:

1. What is the optimal sampling rate for spectrum replication?

The optimal sampling rate for spectrum replication is dependent on the specific application and the desired level of accuracy. In general, a higher sampling rate will result in a more accurate replication of the original signal, but will also require more storage and processing power. Therefore, the optimal sampling rate must be determined based on the trade-off between accuracy and resources.

2. How is the optimal sampling rate calculated?

The optimal sampling rate is typically calculated using the Nyquist-Shannon sampling theorem, which states that the sampling rate must be at least twice the highest frequency component of the signal. This is known as the Nyquist rate. However, in order to accurately replicate a signal, it is recommended to use a sampling rate that is higher than the Nyquist rate.

3. What factors affect the optimal sampling rate?

The optimal sampling rate can be affected by various factors such as the bandwidth of the signal, the desired level of accuracy, the available resources, and the specific application. Additionally, the type of signal being sampled (analog or digital) and the presence of noise can also impact the optimal sampling rate.

4. Can the optimal sampling rate change over time?

Yes, the optimal sampling rate can change over time. This is because the optimal sampling rate is dependent on the specific signal being sampled and the desired level of accuracy. As the signal or the requirements for accuracy change, the optimal sampling rate may also need to be adjusted.

5. What are some potential consequences of using an incorrect sampling rate for spectrum replication?

If an incorrect sampling rate is used for spectrum replication, it can result in a loss of accuracy and fidelity in the replicated signal. This can lead to errors and inaccuracies in the analysis or processing of the signal, potentially impacting the overall results and conclusions drawn from it. In some cases, using a sampling rate that is too low can also result in signal distortion and aliasing, which can further affect the accuracy of the replication.

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