Fourier transform of triangular function

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Discussion Overview

The discussion revolves around finding the Fourier transform of a triangular function defined piecewise. Participants explore the relationship between triangular and rectangular functions, particularly through convolution, and seek clarification on identifying the specific rectangular functions related to the given triangular function.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant presents a triangular function defined in a piecewise manner and requests assistance in finding its Fourier transform.
  • Another participant suggests that a triangular function can be expressed as the convolution of two rectangular functions and mentions the relationship between convolution in the time domain and multiplication in the Fourier domain.
  • A participant expresses difficulty in identifying the specific rectangular functions related to the triangular function in question.
  • A further suggestion is made to plot the triangular function and examine its endpoints to understand the convolution process better.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the identification of the rectangular functions related to the triangular function, indicating that multiple views and uncertainties remain in the discussion.

Contextual Notes

There are unresolved aspects regarding the specific rectangular functions that relate to the triangular function, as well as potential assumptions about the properties of convolution and Fourier transforms that are not explicitly stated.

tronxo
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Im kind of stuck in one of my signals problems. A triangular function defined as: V(t)= (-A/T)t + A when 0< t< T; V(t)= (A/T)t + A when -T< t< 0; otherwise, the function is 0. I have to find the Fourier transform of this function. Could anyone help me??
 
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A triangle function is the convolution of two rectangle functions. You presumably already know what the FT of a rectangle function is, and you know how convolution in the time domain relates to multiplication in the Fourier domain.

- Warren
 
Last edited:
thank you for ur time, warren, but I am still having problems with it. The problem is, even though i know, as you say before, that a triangle function is the convolution of two rect functions, i don't know how to identify which rect functions are related to this particular example.
thank you again, Alex
 
Plot the triangle function, and look at its endpoints. Notice that when you convolve two functions with endpoints (a, b) and (c, d), the resulting convolution has endpoints (a+b, c+d).

- Warren
 
Thanks again
Alex
 

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