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I have an aperiodic signal $v_{out} = e^{-t} u(t)$ (real exponential signal) from discharging capacitor.

I was trying to plot using MATLAB 15 seconds of this signal in time domain? I am thinking how to plot because I donot know $u(t)$. But I am seeing many sources they involve the term $u(t)$ and the Fourier transform is independent of $u(t)$.

I found the Fourier transform $V_{out}$ of $v_{out}$ to be $\frac{1}{1+j\omega}$ where $\omega = \frac{2\pi}{T}$.

$|V_{out}(j\omega)| = \frac{1}{1 + \omega^2} $

How do I plot the magnitude spectrum?(Is it the plot betwen $|V_{out}(j\omega)|$ and $\omega$?)

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  • $\begingroup$ your equation is not fully formed without defining your symbols. t is most likely time but you need to define u. My guess would be that u is a constant, otherwise you would have a multivariable equation which does not have a single fourier transform. If u is constant you need to plot a time series using a constant and a time t for t=0-15 seconds, you can then fft that signal to get a spectrum. $\endgroup$ – PAK-9 Apr 8 at 22:50
  • $\begingroup$ In this kind of context, u(t) is often the Heaviside step function. And yes, you got the right thing for what you'd have to plot for the magnitude spectrum. $\endgroup$ – SleuthEye Apr 9 at 2:14

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