Discrete Fourier Transforms of Signals

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SUMMARY

The discussion focuses on the application of the Discrete Fourier Transform (DFT) to analyze the signal defined by the equation \(x(t) = -17 - 9\sin(4\pi t) + 2.6\sin(8\pi t) - 4\cos(10\pi t)\). The participant emphasizes the importance of selecting a sampling frequency of at least 10 Hz to avoid aliasing, as it must be twice the highest frequency component present in the signal. The participant seeks clarification on how to select and plot the appropriate samples from the signal.

PREREQUISITES
  • Understanding of Discrete Fourier Transform (DFT)
  • Knowledge of signal sampling theory
  • Familiarity with trigonometric functions in signal processing
  • Experience with plotting data in a programming environment
NEXT STEPS
  • Research the Nyquist-Shannon sampling theorem
  • Learn how to implement the Fast Fourier Transform (FFT) using Python's NumPy library
  • Explore techniques for visualizing sampled signals using Matplotlib
  • Study the effects of aliasing in signal processing
USEFUL FOR

This discussion is beneficial for signal processing students, electrical engineers, and anyone involved in analyzing or visualizing time-domain signals using Fourier analysis techniques.

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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