Using MATLAB to plot the input and the magnitude spectrum of the signal

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 $$\omega$$?)

• 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. – PAK-9 Apr 8 at 22:50
• 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. – SleuthEye Apr 9 at 2:14