The Laplace transform
the Laplace transform converts integral and di®erential equations into
algebraic equations
this is like phasors, but
² applies to general signals, not just sinusoids
² handles non-steady-state conditions
allows us to analyze
² LCCODEs
² complicated circuits with sources, Ls, Rs, and Cs
² complicated systems with integrators, di®erentiators, gains
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
The Laplace transform
the Laplace transform converts integral and di®erential equations into
algebraic equations
this is like phasors, but
² applies to general signals, not just sinusoids
² handles non-steady-state conditions
allows us to analyze
² LCCODEs
² complicated circuits with sources, Ls, Rs, and Cs
² complicated systems with integrators, di®erentiators, gains
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)
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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