Laplace Transform 3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the entire w . axis, which of the following two statements are true: The Fourier Transform for x(t) does not exist. The Fourier Transform for x(t) exists. The Fourier Transform for x(t) exists provided that x(t) is absolutely integrable, if not then it does not exist. The system is unstable. The system is stable. There is not enough information to determine existence or non-existence of...
Find the Laplace transform of the function f(t). f(t) = sínztif25tS8; f(t):0if t < 2 or if t > 8 Click the icon to view a short table of Laplace transforms. F (s) =
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+ Uyy=0,- << ,y>0, with the boundary conditions u(1,0) = f(t), - <I< u(x,y) +0,31 +0,+0, is given by r(2, y) == Love you > 0. Hint: 1. Take Fourier transform on the variable r, 2. Observe U(k, y) +0 as y → 00, 3. Use pt {e-Mliv = Vice in
Please show work! (1 point) Find the Laplace transform F(s) of f(t) { O, t<6 5 sin(at), 6<t<7 0, t> 7 F(8)
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
4-6. Using the Fourier transform integral, find Fourier transforms of the following signals: (a) xa(1)-1 exp(-α) u(t), α > 0; (b) xb(t) = u(t) u(1-t);
29.9) Compute the Fourier transform of the periodic function f(t) to prove the equation shown below: 29.9. Let f(t) = iftl > T. 0 Show that f(w) =
Determine Laplace Transform of f(t) = e-3* u(t) for Re(s + 3) >0. s S + 3 1 S + 3 O 1 S-3 3 S- 3
Find the Fourier Transform of the triangular pulse _(1 + t for -1<t < 0 x(t) = (1 - t for 0 <t<1