1. A certain system has the following frequency response, 2(1 x 106(ja)2) H(ja)i2 + 500jw +...
Please explain every step as clearly and detailed as possible. B Frequency Response Modeling Frequency response modeling of a linear system is based on the premise that the dynamics of a linear system can be recovered from a knowledge of how the system responds to sinusoidal inputs. (This will be made mathematically precise in Theorem 13.) In other words, to determine (or iden- tify) a linear system, all one has to do is observe how the system reacts to sinusoidal...
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...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a particular input x(t) this system is observed to produce the output y(t) = e-ºut) - e-stutt) i) Determine x(t). ii) Is this system stable? Explain your reasoning. iii) Plot the magnitude and phase responses of H (jw).
(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....
Question 3 A filter has a unit-impulse response h(t)=0.5e-2'u(t). an (i) Find the frequency response H(jo). (ii) Determine an expression for the steady-state response of the filter to v> 02 sáng)
An LTI system has the frequency response H(o) Tja,+3)(jo+41 Τω+5) Compute the output if the input is x()-2cos (5t). 2
A continuous time system H has the frequency response H(jω) = 4π / (4π + jω) . a) Find and plot the magnitude as a function of radial frequency. b) Find and plot the phase as a function of radial frequency. c) Using H(jω), find the output y(t) for the input x(t) = 4cos(4πt) + 4cos(12πt)
s -3 +4i s 4+3i 1+0.707 1 b) What is the gain, K, associated with that point? Ans: Problem 3: A system is characterized by the following differential equation: If the input is x sinSt, use the frequency response method to determine the steady-state response of the output, yss(t). In showing your work, clearly identify expressions for G(s) Y(s)/X(s), G(jo), [G(jo) l and ф(co). s -3 +4i s 4+3i 1+0.707 1 b) What is the gain, K, associated with that...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2 -40 -60 o-45 2 -90 O-135 -180 10 10 10 Frequency (rad/s) Find the steady state response of the system y$s (t), results from the sinusoidal input as: u(t) -2 sin(3t) Find the steady state response of the system yss (t), results from the sinusoidal input as: u(t) - 5 sin(10t) a) b) c) Find the input u(t) that results into a sinusoidal steady...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...