Math Problem Statement
use direct integration to find the Fourier transform G(f) of the signal g(t) (Note: the unit rectangular function has a range between -1/2 and 1/2: g(t)= Π(t-1)-5exp(-2|t+3|)
Solution
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Math Problem Analysis
Mathematical Concepts
Fourier Transform
Signal Processing
Rectangular Function
Exponential Decay
Formulas
Fourier Transform: G(f) = ∫ g(t) e^{-j2πft} dt
Unit Rectangular Function: Π(t-1)
Exponential Decay Function: exp(-2|t+3|)
Theorems
Fourier Transform Theorem
Integration by Parts
Suitable Grade Level
Undergraduate Engineering or Mathematics
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