An LTI system has the frequency response H(o) Tja,+3)(jo+41 Τω+5) Compute the output if the input...
1. An LTI system has the transfer function (or frequency response) H(u)- a) What is the magnitude of H()? b) What is the phase of H(u)? c) Determine the impulse response of this system. d) Find the differential equation between the input and output of this system. e) What is the output of the system to the input x()c
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
(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....
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t) 5. (12 points) Consider a continuous-time LTI system whose frequency response is...
Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI system for-oo < nく00. Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input to the system is zin] = 5 + 20 cos(0.5mn + 0.25m) + 108[n-3]. Use superposition to determine the corresponding output vin] of the LTI...
5. (30 pts) If the input to an LTI system is zinl (ulml, the output is (a) (15 pts) Find the frequency response of the system, H(e). (b) (10 pts) Find the impulse response hln). (c) (5 pts) Use LCDE to represent the system.
Q5. The measured input-output pair of for an LTI system is observed as follows: LTI system imput: x(t)-1+2cos(t)+5cos (2t)+4cos(t) LTI system output: y(t)-3+cos(t) +6cos(3t) For a new input x(t) = 1+2*cos(t)+5.5*cos(2t)+4*cos(3t), the conrespondding output is observed in the form of y (t)-A+Bcos(t)+Ccos (2t)+Dcos(3t). Determine the values of coefficients of A, B, C, and D A- D- Submit Answer Tries 0/3
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine ??(??) and ??(??) and the ROCs B. (3 points) Using the convolutional property of the Laplace transform, determine ??(??), the Laplace transform of the output, ??(??) C. (3 points) From the answer of part B, find ??(??) 9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...