Determine the Laplace transform, F(s), of the following time signal.
Solution
we\'ll be interested in signals de¯ned for t ¸ 0
the Laplace transform of a signal (function) f is the function F = L(f)
de¯ned by
F(s) =
Z 1
0
f(t)e¡st dt
for those s 2 C for which the integral makes sense
² F is a complex-valued function of complex numbers
² s is called the (complex) frequency variable, with units sec¡1; t is called
the time variable (in sec); st is unitless
² for now, we assume f contains no impulses at t = 0
common notation convention: lower case letter denotes signal; capital
letter denotes its Laplace transform, e.g., U denotes L(u), Vin denotes
L(vin), etc..
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Determine the Laplace transform, F(s), of the following time signal..pdf
1. Determine the Laplace transform, F(s), of the following time signal.
Solution
we'll be interested in signals de¯ned for t ¸ 0
the Laplace transform of a signal (function) f is the function F = L(f)
de¯ned by
F(s) =
Z 1
0
f(t)e¡st dt
for those s 2 C for which the integral makes sense
² F is a complex-valued function of complex numbers
² s is called the (complex) frequency variable, with units sec¡1; t is called
the time variable (in sec); st is unitless
² for now, we assume f contains no impulses at t = 0
common notation convention: lower case letter denotes signal; capital
letter denotes its Laplace transform, e.g., U denotes L(u), Vin denotes
L(vin), etc.
