Finding original signal, given signal obtained by sampling

In summary, the discrete-time signal x(n) = 3.9 cos(0.80πn + 0.2π) was obtained by sampling a continuous-time signal x(t) at a sampling rate of 578.4 samples/sec. To find possible expressions for x(t), the frequency was determined by setting -2*pi*fo/fs = 0.8*pi, resulting in fo = 231.36. Possible frequencies for x(t) are fo +- fs*k, where k is an integer.
  • #1
Jd303
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Let, x(n) = 3.9 cos(0.80πn + 0.2π) be the discrete-time signal obtained by sampling a continuous-time signal x(t) at a sampling rate of 578.4 samples/sec. Find possible expressions for x(t).

Hey all,
I am quiet unfamiliar with this type of question, and haven't been able to put anything together that makes sense.
I know that the amplitude and phase will stay the same, however figuring out possible frequencies has got me stuck. Would greatly appreciate anyone that is able to walk me through or point me in the right direction for this problem. Thanks in advance!
 
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  • #2
Just had a breakthrough, needed to get away from the problem and then look at it again.
Just in case anyone wants to correct me:
-2*pi*fo/fs = 0.8*pi
-Therefore fo = 231.36
-Therfore possible frequencies are fo +-fs*k where k is an integer
 

1. What is the concept of sampling in signal processing?

The concept of sampling in signal processing is the process of converting a continuous signal into a discrete signal by taking a sample of the signal at regular intervals. This is done for various reasons, such as for easier storage and transmission, or to apply digital signal processing techniques.

2. How does the sampling rate affect the original signal?

The sampling rate, also known as the sampling frequency, is the number of samples taken per second. A higher sampling rate means more samples are taken, resulting in a more accurate representation of the original signal. Conversely, a lower sampling rate can result in loss of information and distortion of the original signal.

3. Can the original signal be accurately reconstructed from a sampled signal?

Yes, the original signal can be accurately reconstructed from a sampled signal, as long as the sampling rate is high enough and the Nyquist-Shannon sampling theorem is satisfied. This theorem states that the sampling rate must be at least twice the highest frequency component of the original signal in order to accurately reconstruct it.

4. How can we find the original signal from a sampled signal?

To find the original signal from a sampled signal, we can use a process called interpolation. This involves using mathematical techniques to estimate the values of the original signal between the sampled points. Different interpolation methods can be used, such as linear or cubic interpolation, depending on the nature of the signal.

5. Are there any limitations to finding the original signal from a sampled signal?

Yes, there are limitations to finding the original signal from a sampled signal. If the sampling rate is too low, or if the original signal contains high frequency components that exceed the Nyquist frequency, the reconstruction may not be accurate. Additionally, if the sampled signal is corrupted by noise or other interference, it may be difficult to accurately retrieve the original signal.

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