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24題拉普拉斯轉換 (i.e. 拉普拉斯變換 or 拉氏轉拉氏轉換)
L{t^n} (用級數)
L{sin(bt)}, L{cos(bt)}
L{sinh(bt)}, hyperbolic sine
L{cosh(bt)}, hyperbolic cosine
L{U(t-a)}, unit-step function
L{Πa,b(t)}, the window function
L{δ(t-a)}, Dirac Delta function
L{f(t-a)U(t-a)}, shifting theorem in the t-domain
part 2
L{(t-2)^2*U(t-2)} vs. L{t^2 U(t-2)}, 拉普拉斯轉換例子
例子 L{sin(t)} vs L{sin(bt)}
L{e^(at) f(t)}, shifting theorem in the s-domain
L{e^(3t)cos(2t)}
L{tsin(bt)}
的分母應該是(s^2+b^2)^2
L{sin(t)/t}=pi/2-tan^-1(s)
積分sin(t)/t, 積分sin(t)/(te^t), 積分sin(e^t)?
L{integral of f(u)}
L{f(t)*g(t)}, the convolution theorem
L{sqrt(t)}, ft. Gamma function