Laplace Transform 7. For a system with a rational Laplace Transform H(s), causality of the system...

Question

Question

Laplace Transform 7. For a system with a rational Laplace Transform H(s), causality of the system is equivalent to the ROC being a right sided

Answer 1

Answer #1

It is TRUE, that if x(t) is right sided and it's Laplace transform X(S) is rational , then the ROC in S- plane is right most pole.

An example is provided below:

ROC to the right of the pole at S=.-3. Answer Let, An expression of H(s) may (firesponds to different signals Signals with wi

Similarly, if x(t) is left sided and it's Laplace transform X(s) is rational , then the ROC in S - plane left of the leftmost pole.

Answer 2

Similar Homework Help Questions

Laplace Transform 5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what...

Laplace Transform 5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal...

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...
Signal and Systems Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response...

Signal and Systems 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)...

12 Problem la (10 points) Find the inverse Laplace transform of: Fo(s) the ROC is defined...

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...
Laplace Transform 3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the...

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...
6 and 7 please le jo OSIST otherwise Find the Laplace transform of x(). Find the...

6 and 7 please le jo OSIST otherwise Find the Laplace transform of x(). Find the Laplace transform X(s) and sketch the pole-zero plot with the ROC for the following signals x(i): (a) x -e () + e- () (b) X(= () + (-1) (c) x(1) eu (1) + (-1)

8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the...

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...

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...
Signal and Systems 8 + If Problem la (10 points) Find the inverse Laplace transform of:...

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:

Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation...

Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...