Solving Sampling Frequency Exam Questions

In summary, the conversation discusses a question about sampling frequency and bandwidth in relation to modulated signals. The first question asks for the sampling frequency of y(t) and z(t), while the second question asks about the minimum sampling frequency for recovering a signal with a specific bandwidth and filter. The solution involves considering the modulating technique and using the Nyquist-Shannon criterion.
  • #1
nightworrier
8
0
hello everyone,

I have an exam question about sampling frequency. Actually i really don't get the concept. I have limited sources.
Question:

Bandwith of x(t) 10 kHz
y(t) obtained modulating x(t) with a sinus wave with frequency 30 kHz.
y(t) sampled
a) What is the sampling frequency of y(t) ?
b) z(t)=y(t)+s(t) -> bandwith of s(t) = 40 kHz, what is the sampling frequency of z(t) ?

Could you help me to find a solution ?
 
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  • #2
It depends on the modulating technique. If it is amplitude modulation, then the spectrum of y(t) will stretch from 10khz to 40khz, thus for correct sampling(Nyquist-Shannon criterion) you need to sample y(t) at a freq of at least 80khz.
As for z(t) the answer is the same as above, since the spectrum of y+s doesn't extend further than 40khz.
Hope this helps.
 
  • #3
Thank you for your answer but i have another question if you can help me , i will be appreciate...

Consider x1(t) and x2(t) with bandwith B1=10 kHz and B2=15kHz.
The signal y(t)=x1(t)-x2(t) is sampled.

Find the minimum sampling frequency for which it is possible to recover the signal y(t) from its samples if the filter is used for reconstruction is ideal or if it has a transfer function which is constant in [-20kHz, 20kHz] and bandwith 35kHz
 

What is sampling frequency and why is it important in scientific research?

Sampling frequency refers to the number of samples or data points collected per unit of time in a measurement or experiment. It is important in scientific research because it determines the accuracy and precision of the data collected, as well as the ability to detect patterns and trends in the data.

How do I determine the appropriate sampling frequency for my experiment?

The appropriate sampling frequency depends on the nature of the data being collected. Generally, a higher sampling frequency is recommended for data that changes rapidly or is highly variable, while a lower sampling frequency may be sufficient for data that changes slowly or is less variable. It is also important to consider the limitations of the equipment being used and the resources available for data analysis.

What are some common errors that can occur when determining sampling frequency?

One common error is using too low of a sampling frequency, which can result in missing important data points and inaccurate conclusions. Another error is using too high of a sampling frequency, which can lead to excessive data and difficulties in data analysis. It is important to strike a balance and choose a sampling frequency that is appropriate for the specific research question and data being collected.

What is the relationship between sampling frequency and signal frequency?

Sampling frequency and signal frequency are closely related. In order to accurately capture a signal, the sampling frequency must be at least twice the signal frequency, according to the Nyquist-Shannon sampling theorem. This means that the sampling frequency must be high enough to capture the highest frequency component of the signal in order to avoid aliasing and distortion.

Can I increase the sampling frequency after collecting data?

No, the sampling frequency cannot be increased after data has been collected. It is important to determine the appropriate sampling frequency before beginning an experiment or measurement. However, if the data collected does not meet the desired level of accuracy, it may be possible to repeat the experiment with a higher sampling frequency.

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