Signal and Systems Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response...
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
. Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = 365+1096+4) (.e. f(t) is causal) lim f(t) = 00 1-0 limf(t) = 1. 10x4 lim f(t) = 0 • limf(t) cannot computed since sF(s) is not analytic. None of these choices is correct. -0 . t-0 t+0 . b) (2 points) What is the final value of time function f(t) corresponding to the one 40 sided...
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...
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:
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
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:
signal and system
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2
F(s), (10 points: 5+5) Obtain the Laplace transform for each of the functions given below. ĢIT when the Laplace transform of the function with a time shift of T is given by Aft-T) 1t-T)]-F(s)e ) |0 0S1<1,123 0 f(t) = t-1 1ste2 1 22
F(s), (10 points: 5+5) Obtain the Laplace transform for each of the functions given below. ĢIT when the Laplace transform of the function with a time shift of T is given by Aft-T) 1t-T)]-F(s)e ) |0...
need asap
1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
4. (2 marks) Determine (i) the Laplace transfer function, (ii) the impulse response function, and (ii) the input-output relationship (in the form of a linear constant-coefficient differential equation) for the causal LTI systems with the input-output pairs: a) x(t)-41(t) and y(t)-tu(t) + e-2tu(t). b) x() e2tu(t) andy(t)2u(t-4).