The signal x(t)=e^(-|t| ) is defined for all values of t. a. Plot the signal x(t

Question

The signal x(t)=e^(-|t| ) is defined for all values of t.
a. Plot the signal x(t) and determine if this signal is finite energy. That is, compute the integral

int_(-infinity)^infinity |x(t)|^2 dt
and determine if it is finite.
The work I currently have:

x(t)=int_(-infinity)^0 e^t )^2 +int_0^infinity (e^(-t) )^2 =
?_(-?)^0 e^2t +?_0^? e^(-2t) =
[e^(3t/3) ]_(-?)^0+[e^(3t/3) ]_0^?=
(0-1/3)+(-1/3+0)=-2/3=finite

b. If you determine that x(t) is absolutely integrable or that the integral
int_(-infinity)^infinity |x(t)|^2 dt
is finite, could you say that x(t) has finite energy? Explain why or why not.
Hint: Plot |x(t)| and |x(t)|^2.
Please verify my work and help me with part b. Thank you.

Explanation / Answer

The a part is correct to my knowledge. Yes one can conclude from the finiteness of the integral that energy is finite.Since the total sum of energy is finite over a time t.One can form a cauchy sequence of finite energies at a particular time t

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