Fourier Transform - Rectangular Function Help

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SUMMARY

The discussion focuses on applying the Fourier Transform to the rectangular function defined as X(t) = 5Rect((t+2)/4). The user seeks guidance on substituting values into the Fourier Transform equation, specifically F(ω) = ∫_{-∞}^{∞} f(t)e^{jωt} dt. The rectangular function is defined as Rect(t) = {A, if -t/2 ≪ τ ≪ t/2; 0, otherwise}. The conversation emphasizes the importance of understanding the substitution process for the Fourier Transform of modified rectangular functions.

PREREQUISITES
  • Understanding of Fourier Transform principles
  • Familiarity with rectangular functions and their properties
  • Basic knowledge of integration techniques
  • Ability to manipulate mathematical expressions involving complex numbers
NEXT STEPS
  • Study the Fourier Transform of standard rectangular functions
  • Learn about the properties of the rectangular function in signal processing
  • Explore integration techniques for complex exponential functions
  • Review examples of Fourier Transform applications in engineering
USEFUL FOR

Students in signal processing, engineers working with Fourier analysis, and anyone seeking to understand the application of Fourier Transform to rectangular functions.

soharca
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1. Hi! I am new at this forum, and english is not my native language,
so, I hope I can make myself clear. A teacher send us a list of activities,
but he did not give us the theory about it (the theoretical class). So, I have
read a few things on the internet and I have solved some exercises. I want
to clearly state that I don't pretend to anyone do the exercise, but if you could
guide me, I will appreciate.

X(t)= 5Rect((t+2)/4)

Homework Equations



F(ω)=int^{\∞}_{-\∞}f(t)e^{jwt}dt (Fourier Transform definition)

Rect(t)=Rect(t)={(A ,if-t/2≪τ≪t/2 (Rectangular function definition)
0,if other)

The Attempt at a Solution



I just need to know how to start.
I don't know where to substitute the 5 or the (t+2)/4Sorry to bother.
And thank you very much.
 
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