Laplace Transform 12 12 + s+12 s+8 Problem 4 (15 points) : Find the inverse Laplace...
Signal and Systems 8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the ROC is defined as: -12 <Re(s) <0 Identify terms as right sided or left sided. S+12 Re(s) < 0 Re(s) >-12 Х X -12 0 Problem 1b (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why:
8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the ROC is defined as: -12 <Re(s) <0 Identify terms as right sided or left sided. S+12 Re(s) < 0 Re(s) >-12 Х X -12 0 Problem 1b (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why:
12 Problem la (10 points) Find the inverse Laplace transform of: Fo(s) the ROC is defined as: -12 < Re(s) <0 Identify terms as right sided or left sided. 8 +- If S S+12 Re(s)< 0 Re(s) >-12 X X -12 0 Problem lb (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why: Given the unilateral Laplace transform of the impulse response for a causal system H(S) = Determine h(t) the impulse response? Hint synthetic...
7. Find the inverse Laplace Transform of X(so2 with ROC-1< Rels) 1.
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem: 1, y' + 9 = 0<t<T 0,7 <t< y(0) = 5, y'(0) = 4
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...
1. (2 points) Using the definition, find the Laplace Transform of the function: e21, 0<t<3 f(t) = 3<t
Ordinary Differential Equation Problem (16) <6> Find the Laplace transform of fo + 2sin 4r) 052
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 $3 (s2+4) 2 >(t)= (s2+4) s3
Please answer all questions with math detail 3. (21 points) Laplace Transform (a) (15 points) Find the Laplace transforms of the following signals and determine their region of convergence sinwot)-iu i. f(t) -i, e-2(t-3 2<t otherwise (b) (6 points) The Laplace transform of a causal signal x(t) is given by X (s) = s2 , ROC: Re{s) > -1 Which of the following Fourier transforms can be obtained from X(s) without actu- ally determining the signal x(t)? In each case,...