Sketching Signal x(t): 2^(-t*u(t))

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SUMMARY

The discussion focuses on sketching the signal defined by the function x(t) = 2^(-t * u(t)) over the interval (-1 < t < 1). The function is analyzed as a piecewise function, where x(t) equals 1 for t < 0 and 2^(-t) for t > 0. The square of the function, x(t)^2, is also derived, resulting in 1 for t < 0 and 2^(-2t) for t > 0. The integration of x(t)^2 from -1 to 1 is split into two separate integrals, one from -1 to 0 and the other from 0 to 1, facilitating the calculation of the area under the curve.

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Homework Statement



Sketch the signal:
x(t) = 2^(-t*u(t)) over (-1 < t < 1)

The Attempt at a Solution


Attached is an excel fine with my work out. I want to know is it is correct.
 

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It is simplest to think of this as a piecewise function
[tex]x(t) = \begin{cases}<br /> 1, t < 0 \\<br /> 2^{-t}, t>0<br /> \end{cases}[/tex]
then
[tex]x(t)^2 = \begin{cases}<br /> 1, t < 0 \\<br /> 2^{-2t}, t>0<br /> \end{cases}[/tex]
so when you integrate x(t)^2 from -1 to 1, it breaks apart into two integrals. One is from -1 to 0 of 1, and the other is from 0 to 1 of 2^{-2t}.
 

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