Discrete Fourier Transforms of Signals

AI Thread Summary
The discussion focuses on the application of the Discrete Fourier Transform (DFT) to a given signal, emphasizing the importance of selecting an appropriate sampling frequency to avoid aliasing. The participant suggests a sampling frequency of 5Hz for the signal defined as x(t) = -17 - 9sin(4πt) + 2.6sin(8πt) - 4cos(10πt), which raises questions about the number of samples and their plotting. There is confusion regarding the correct number of samples to plot, with a mention of needing four samples and a query about the possibility of having 2.5 samples. The participant seeks clarification and additional insights on these points. Overall, the thread highlights key considerations in signal sampling and representation in the context of DFT.
mintsnapple
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Homework Statement


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Homework Equations

The Attempt at a Solution



I'd like to see if I have the right line of thinking in my solutions:
a. The sampling frequency should be such that no aliasing or folding occurs, so it should be twice the frequency of the original signal.
$$x(t) = -17 -9sin(4\pi t) + 2.6sin(8\pi t) - 4cos(10\pi t)$$, I think sampled at 5Hz.
b. There should now be four samples...but which four samples should I plot?
c. There should be 2.5 samples right? Again how should I plot?
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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