Find CTFT Using MatLab: A Guide

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In summary, the conversation discusses how to find the CTFT of a function using MatLab. It is mentioned that MatLab has a built-in function called fft for finding the fast Fourier transform, but it may not work for finding the CTFT. One possible solution is to use symbolic math capabilities or a package like Mathematica.
  • #1
olen501
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Does anyone know how to find the CTFT of a function using MatLab? I know MatLab has a built in function called fft that finds the fast Fourier transform, but I don't know how to use the fft to find the CTFT. Can anyone help me out?
 
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  • #2
You can do something like:

x = cos(2*pi*f*t);
ft = fftshift(fft(x));

Then you must plot over the proper frequency range. This is most likely why you can't work with fft and get the right results.
 
  • #3
When you say CTFT, you mean the Continous-Time Fourier Transform? The only way to do that on a computer is using symbolic math. You can't directly represent a continuous function inside the computer, and so you can't directly compute its Fourier Transform. So, supposing you have an expression for the function in question, you can feed that into the symbolic math toolbox, and have it give you an expression for the answer. I haven't used Matlab's symbolic math capabilities very much, so I can't comment further, but you might also just use The Integrator ( http://integrals.wolfram.com/index.jsp ). The downside to these approaches is that they tend not to be terribly good at simplifying the results, so you're apt to get a huge string of special functions that all end up cancelling each other out. Often, the process of simplifying the output of these symbolic math systems can be as laborious as simply doing the integral yourself in the first place. They are good resources if you're stuck or want to check your answers, though...
 
  • #4
Yes, better to use a package designed with symbolic computations in mind...like Mathematica.
 
  • #5
Thanks
 
  • #6
thanks
 

1. What is CTFT and why is it important?

CTFT stands for Continuous-Time Fourier Transform, which is a mathematical tool used to analyze signals in the frequency domain. It is important because it allows for the decomposition of a signal into its constituent frequencies, which can provide valuable insights for signal processing and analysis.

2. How can MatLab be used to find CTFT?

MatLab is a powerful software tool for scientific computing and data analysis. It has built-in functions that can be used to calculate the CTFT of a signal, such as the fft() and fftshift() functions. These functions can be applied to the time-domain signal to obtain its frequency-domain representation.

3. What are the basic steps for finding CTFT using MatLab?

The basic steps for finding CTFT using MatLab are as follows:

  1. Define the time-domain signal of interest.
  2. Apply the fft() function to the signal to obtain its frequency-domain representation.
  3. Use the fftshift() function to center the frequency-domain representation around zero frequency.
  4. Plot the magnitude and phase of the frequency-domain representation using the abs() and angle() functions.
  5. Interpret the results to gain insights into the signal's frequency content.

4. Are there any limitations to using MatLab for finding CTFT?

While MatLab is a powerful tool for many scientific applications, it does have some limitations when it comes to finding CTFT. The fft() function assumes that the signal is periodic, which may not always be the case for real-world signals. Additionally, the accuracy of the results may be affected by the sampling rate and length of the signal.

5. Can MatLab be used to find CTFT of non-continuous signals?

Yes, MatLab can also be used to find the CTFT of non-continuous signals, such as discrete signals. In this case, the fft() function can be applied to the discrete signal to obtain its discrete-time Fourier transform (DTFT), which is a discrete version of CTFT. MatLab also has functions for calculating other types of Fourier transforms, such as DFT and FFT, depending on the specific needs of the analysis.

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