Composite SystemsConsider the following impulse responses of two LTI systems:h(t) = 8(t - 2),g(t) = e-alt, a € R+(a) Find H(w) and G(w), the frequency responses (CTFT) of the systems.(b) Consider interconnected LTI systems with impulse responses h(t) and g(t):System 1, with overall impulse response of $₁(t):x(t)System 2, with overall impulse response of s₂(t):x(t)(c) Nowh(t)supposeg(t)h(t)y₁ (t)g(t)Find the impulse responses s₁(t) and s₂(t). Also find their respective fre-quency responses S₁ (w) and S₂(w).x(t) = eiwot+Y₂(t)Calculate the output y(t) of the two systems S₁ and S₂ when given x(t) as aninput.Hint: Convert x(t) to the frequency domain, and feed it through the com-posite system before taking the inverse transform of the result. As a furtherhint, note that convolution in the time domain is equivalent to multiplicationin the frequency domain.

Given:Impulse response of two LTI systems, we are required to:a) find CTFT of h(t) and g(t). b) If…

Answered: Composite Systems Consider the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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1. -1 H(w) %3D jw - 2 (a) Find the impulse response and determine whether the system is causal. (b) Find the zero-state response to input e-tu(t) and to input e'u(-t).
For the given LTI system: y[n] = x[n + 5] + 2y[n-1], find the impulse response. Is the system casual? Stable? Explain your answers in terms of the impulse response characteristics.
1. For the following system, use root locus techniques to design a compensator to satisfy the following criteria: a. -0.8, b. Zero steady-state error to step input. K(s + 2)(s + 1) (s – 2)(s – 1) R(s) + C(s)
OBJECTIVE 7-3 SECOND-ORDER CIRCUIT ANALYSIS (SECTS. 7-5, 7-6, 7-7) Given a second-order circuit: (a) Find the circuit differential equation. (b) Find the circuit natural frequencies and the initial condi- tions (if not given). (c) Find the zero-input response. (d) Find the complete response for a step function input. See Examples 7-17, 7-18, 7-20 to 7-23, 7-24, and 7-26 and Exercises 7-25, 7-27, 7-29 to 7-31 and 7-33. S7-37 Find the v(t) that satisfies the following differential equa- tion and initial conditions: dv(t) du(t) di² dt +6- +48u(t)=0, v(0)=0 V, dv(0) dt = 48 V/s
In order to reduce the steady-state error of a system, a lag compensator was designed as shown. Determine the steady-state errors for a ramp input before and after adding the lag compensator. Hint: use Kv R(s) Select one: O a. 1 and 0.3 O b. 1 and 0.2 O c. 1 and 0 O d. 2 and 1 O e. 2 and 0.5 S+ 0.1 s+0.01587 lag compensator 0.7936 2 s(s+ 1)(S + 2) plant C(s)
D Using - transformation. find the impulse response af System desoribed by Sn+ 3, where Sn is a unit impulse function.
An LTI system has an impulse response: h(t) = etu(t - 1) %3D This system is: Select one: O Causal but not stable O Not causal and not stable O Causal and stable O Not causal but stable The convolution of a signal with with a delta function gives: Select one:
(b) The top panel in Figure 1 shows the input and the impulse response of an LTI system. Sketch the output of the system. Note: No mathematical work is needed, use a graphical approach. x(t) h(t) 2 2 1 1 t -5 -1 1 -3 3 y(t) Figure 1: Figure for Problem 1(b).
The impulse response of a LTI system is 8 (t + 1) Is the system causal? O Yes O No answer text provided. O No answer text provided. O No
3) One system consists of 2 DZD systems added consecutively. These DZD systems if the frequency responses are as follows, what is the difference equation shown by this system and the impulse response of this system? 3 - e-/w H;(elw) = 1+ 1 H2(e/w) = 5e-/w 1- 2 jw
b[c] + 0.4b[c - 1] - 0.25b [c - 2] = a[c] - a[c - 1]The linear difference equation above shows the relationship between an input a[c] & output b[c] of a Linear Time-Invariant(LTI) system at a manufacturing plant.Determine the followinga. Impulse responseb. Frequency response of the system
Question 2 Figure 2 represents a block diagram of a discrete time LTI system. Find the impulse response of the system. Then, evaluate the system causality and stability. Prove your answer. 1 w[n] 6. x[n] 3) Σ -y[n] -1 z 2 5 (Σ) z -1 Figure 2

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