Problem 3.6 i) Compute the causal impulse response, h, and the anti-causal impulse response, h, for...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
please provide a complete solution with the correct answer. Let the following causal system be initially at rest, and let h[n] be the impulse response, with z- transform H(zEfS A. 2 2 20.The second point of the impulse response is, hlll- a) 0 b) 1/3 C)1/2d)3/2e)none above Let the following causal system be initially at rest, and let h[n] be the impulse response, with z- transform H(zEfS A. 2 2 20.The second point of the impulse response is, hlll- a)...
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n) and the output y(n) are given as follows 72 42)un-1) y(n)-G)na(n) xnun)
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
Determine the output response y[n] of a causal LTI digital system with an impulse response h[n]=2(0.2)n μ[n] for an input sequence x[n] = 4(0.3)n μ[n]
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
3.21. An LTI system has the impulse response h()-u(t+7)-u(t-8) (a) Determine whether this system is causal (b) Determine whether this system is stable. (c) Find the system response to the input x(f) 8(t-2)-28(t+ 2)
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr