Discrete Fourier Transforms of Signals

In summary, the conversation discusses the optimal sampling frequency for avoiding aliasing or folding in a signal, as well as determining which four samples to plot. The poster also mentions having 2.5 samples and asks for clarification on how to plot them.
  • #1
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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  • #2
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?
 

What is a discrete Fourier transform (DFT) of a signal?

A discrete Fourier transform is a mathematical tool used to decompose a signal into its individual frequency components. It is used to convert a signal from its original time domain representation to a frequency domain representation.

How is a discrete Fourier transform performed?

A discrete Fourier transform is performed by taking a finite sequence of data points and computing the complex-valued Fourier coefficients at discrete frequencies. This is typically done using a fast Fourier transform (FFT) algorithm, which is a computationally efficient method for calculating the DFT.

What is the significance of using a discrete Fourier transform on a signal?

The discrete Fourier transform allows us to analyze the frequency components of a signal, which can provide insights into its underlying properties and behavior. This is useful in a variety of fields, including signal processing, audio and image processing, and data analysis.

What are some applications of discrete Fourier transforms?

Discrete Fourier transforms have many practical applications, including filtering and smoothing of signals, spectral analysis, data compression, and pattern recognition. They are also used in various scientific and engineering fields, such as telecommunications, astronomy, and biomedical imaging.

What are the advantages of using a discrete Fourier transform over other signal processing techniques?

The discrete Fourier transform has several advantages, including its ability to identify specific frequency components in a signal, its computational efficiency through the use of FFT algorithms, and its flexibility in analyzing non-periodic and non-stationary signals. It also allows for easy visualization and interpretation of signal data in the frequency domain.

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