| THEORETICAL INTRODUCTION – THE CONTINUOUS TIME FUNCTION AT THE ORIGIN AND ITS FOURIER TRANSFORM |
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The Continuous Time Exponential Function at the Origin is graphically represented by the figure that follows.
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The function in this object is a decreasing exponential function and its analytical expression is:
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f\left ( t \right )=\left\{\begin{matrix}e^{-at};\, \, t > 0, a> 0\\0;\, \, t< 0\end{matrix}\right.
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The general expression of the Fourier Transform is:
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F\left ( j\omega \right )=\int_{-\infty }^{\infty }f\left ( t \right )\, e^{-j\omega t}dt
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After computing the Fourier Transform of the function, the following expression is determined:
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F\left ( j\omega \right )=\frac{1}{a+j\omega };\, \, a> 0
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This is the expression the simulator uses.
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