The system function of a causal LTI system is1+2-1H(2)(1 – 0.5z-1)(1+ 0.25z¬1)"a) What is the region of convergence of H(z)?b) Is the system stable? Explain.c) Find the z-transform X(z) of an input r(n) that will produce the outputy(n) = -G)(-"u(«) – (G(2)"u(-n – 1).d) Find the impulse response h(n) of the system.

The system function of a causal LTI system is: H(z)=1+z-1(1-0.5z-1)(1+0.25z-1) a) We need to find…

The system function of a causal LTI system is 1+z¬! H(2) = (1 – 0.5z-1)(1+ 0.25z-1)' a) What is the region of convergence of H(2)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input ¤(n) that will produce the output %3D d) Find the impulse response h(n) of the system.

The system function of a causal LTI system is 1+z¬! H(2) = (1 – 0.5z-1)(1+ 0.25z-1)' a) What is the region of convergence of H(2)? b) Is the system stable? Explain. c) Find the z-transform X(z) of an input ¤(n) that will produce the output %3D d) Find the impulse response h(n) of the system.

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...

See similar textbooks

Related questions

Q: A discrete-time signal x[n] is shown in the figure below. Sketch and carefully label each of the…

A: Note: We are authorized to answer one question at a time since you have not mentioned which question…

Q: Question 2: Consider a Linear Time-Invariant (LTI) system with input x(n) and output y(n) related by…

A: Brief description : In the above given question they have mentioned a difference equation which is…

Q: a. Show and explain the ROC of H(z) = (1-z-¹)²(1-z-¹)z³. b. Explain whether the system is causal and…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: for LTI discrete time system described by: y(n)= 0.5 y(n-1) + 0.2 x(n) yl-1) = 0 x(n) = (0.6)" u(n)…

Q: Q1. For each of the following signals, find the z-transform, its poles and zeros, and the region of…

A: a) xan=52nu-5-nu-5-n=1.........(when -5-n>0)X(z)=∑n=-∞∞xanz-n =∑n=-∞-552nz-n…

Q: b) The Z transfom of a LTI discrete time system is represented as: H(z) = 4z-1 1- 11z-1+30z¬2…

Q: Question 9 A signal X(t) = 5-cos 10mt is sampled at the Nyquist rate, starting at t= 0. What is the…

A: Write the expression of given signal,

Q: Obtain through v3 in the given circuit. Assume A = 10 V.

A: For the given circuit the value of the unknown voltages needs to be calculated.The given circuit is…

Q: A) A causal sequence for a system is expressed using the difference question as: y(n) – 2y(n-1) = 2n…

Q: Quation Take the system with the input x, and output y, and the input-output relationship y(n) =…

A: Given, y(n) = x(n) − x(n − 1) + x(n − 2) − x(n − 3)

Q: 31. In a pumped storage scheme of height 400 m, the combined efficiency of the turbine, electric…

Q: )X(z) = 1 – 3z¬1 , Y(z) = 1+ 2z¬² are Z-transforms of two signals x[n], y[n], respectively. A linear…

A: In this question we need to find a output of the system for given input.

Q: below Suppose a bandlimited continuous-time signal f(t) with the spectrum shown -2750 f(t) sampling…

A: What is a sampling of signal? Sampling is the conversion of a continuous-time signal into a…

Q: Given the following two pairs of signals, find the discrete-time convolutions y = x *h for the given…

A: We need to find a convolution of the given signal.

Q: signal. Use the tables of transforms and properties to find the DTFTs of the following x[n] =…

Q: Question 5 (a) What will be the inverse z-transform of the signal? X(z). where, X[z] = z - 10z²-4z+4…

A: CONTINUOUS AND DISCRETE-TIME SIGNALS: Because a signal is a function, we truly mean continuous-time…

Q: Given the Z-transform of a signal by: X(z) = A. x(n) = (0.6)"u[n] x(n)=0.5(0.6)2nu[n] 24-0.6 |z]>…

Q: Question 5. digital system has Z transfer function G(z) nter a: nter k: nter 3: nter 1: = he input…

Q: Consider a system. If for any causal input x[n], the output y[n] is causal, then the system causal.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 11 Using long division, determine the inverse :-transform of 1+2:- X(2) = 1- 2:-1 +z-

A: As per guideline we are supposed to answer only the first question. Kindly repost the question as a…

Q: 0.2: (a)- The R-2R DAC with a 2 bit as b, bo = 01. Draw its cireuit and determine the converted…

A: Digital electronics and signals and systems

Q: Given two discrete-time signals x₁(n) = {0.9 0.5 0.8 1.0 1.5 2.0 ↑ 0.2} and x₂ (n) = {1.0 0.3 0.6…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: (b) An input x(t) as in Figure Q1(a) is passed through an LTI system with impulse response given by…

A: To find the LTI system response y(t)

Q: Q2 Consider the standard second-order system G(s): +25+ a) Write the Laplace transform of the signal…

A: a. The given signal is a piecewise linear function (u(t)) plotted against time in seconds. It has…

Q: Determine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the…

A: Given below clear explanation

Q: - 1 Determine the z-transform of the following signals. (a) x(n) = {3, 0,0.0,0, 6, 1, -4) ()", n2 5…

Q: (c) A causal linear constant coefficient differential equation (LCCDE) is described as 7 yln] - yln-…

Q: The differential equation between input r(t) and output y(t) of a linear time invariant system is…

A: "According to the company's policy we will provide solution for the first three sub-parts of the…

Q: 5. Consider a discrete system, if the input x(n) = (0.6)" u(n) and the impulse response h(n) =…

Q: Need help figureing out question 5. Please show all work

Q: 1 Determine the :-transform of the following signals. (a) x(n) = {3, 0.0.0,0, 6, 1, –4) (b) x(n) =…

Q: A- Find the z-transform and the ROC for each of the following signals: i) x1(n) = 3u(n) – 4(2)"u(n)…

Q: The input to a causal LTI system is x[n] = u[-n – 1]+ G) «In). The z-transform of the output of this…

A: Part a: Write the expression for the sum of the geometric progression of the infinite terms, Here,…

Q: Consider the Z-transform of the impulse response h(n) shown from the figure below. If we define y(n)…

A: SOLUTION:- 1) Hz =0.2251-z-21+0.39z-2-0.16z-4 Hz =0.225z2-1z2z4+0.39z2-0.16…

Q: Question 5. A digital system has Z transfer function G(z) The input signal {un), n ≥ 0, is un =…

A: The given problem is from z transform. The detailed solution is given in the next steps

Q: When the unit step function is applied to the input of the control system given below, the peak time…

A: Unit step input peak time = 0.59 s settlement time =0.88 s. steady state error of the system =10%…

Q: b) if x (1) is used as an input to BIBO L.T.I. system described by: y'-2y =x (t). Find: 1. The…

Q: Consider the Z-transform of the impulse response h(n) shown below. If we define y(n) as the output…

A: We need to determine the impulse and unit step response of the relaxed system described by the…

Q: Task-1: Convert the following difference equations into z transforms: (a) y ( n ) = x ( n – 2) (b) y…

A: Since we are allowed to solve only first question of multiple questions. The below solution contains…

Question

The system function of a causal LTI system is
1+2-1
H(2)
(1 – 0.5z-1)(1+ 0.25z¬1)"
a) What is the region of convergence of H(z)?
b) Is the system stable? Explain.
c) Find the z-transform X(z) of an input r(n) that will produce the output
y(n) = -G)(-"u(«) – (G(2)"u(-n – 1).
d) Find the impulse response h(n) of the system.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Required

VIEW

Step 2: Analysis for ROC

VIEW

Step 3: Calculation for x(n)

VIEW

Step 4: Calculation for impulse response

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Different Types of System and Its Property

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

If there are unit impulses present at f,= ±12kHz and f2= ±8kHz then possible time-domain expression for an SSB signal (f.= 10kHz) is %3D %3D Select one: O a.QusB(t)= cos24 mt O bPLsB(t) = cos16 nt O CPLSB(t)=2cos16 nt O d.Puse(t) =2cos20 nt
x[n] is given as shown below. What is the Z transform of x[n] What is the z-transform of the signal x(n)-na"u(n)? a) az (1+az 1)? (az) ! b) (1-(a2) ')? az 1 c) (1-az )2 az d) (1-(az) ')² e) a and c are correct a b O c d. O e
Let x(n) be a causal sequence with z-transform X(z) whose pole-zero plot is shown below. Sketch the pole-zero plots and the ROC of the following sequence: a) x1(n)=x(2-n) Im(z) b)x2(n)=e" x(n) n 0.5 Re(z) -0,5 -1 0.5 -0.5
Determine the Total Response when x(n)=4(0.5)nu(n)+3(0.75)nu(n) using the Z-transform, given the system described below and its initial conditions.Then considering the given input, what are the energies of the input and the resulting output of the system?
Problem 7 Find the Z-transform of f(n) = (0.5)"rects(n-5)). Be sure to specify the ROC. Problem 8 Find the causal impulse response h(n) via the long division method for H(2) out for 0 ≤ n ≤ 2. = 2:²+ = 22+1.5:-0.5 Problem 9 Find the causal impulse response h(n) via partial fraction expansion method for H(=)= Carry this ²+6: 6:²+2-1'
b) Propose the impulse response for the following system:i) causalii) stableiii) neither stable nor causalFind the region of convergence (ROC) of the Z-transform in each of the above cases.
Please solve all correctly showing ALL the steps and the formulae that is being used from the concepts of Digital Signal Processing.Also find the ROC of i) , ii) and iii)
i got confusd by a signal question. thnk u sir from now
Q2) for LTI discrete time system has an impulse response and input as n+2 n h(n) = (0.4) u(n) x(n) = (0.5)" u(n+1) find 1. The output response y(n) using Z-transform 2. ROC for X(z) , H(z) and Y(z)
Please help with part d and e.
Please help me understand all parts.
This subject is digital signal processing of ece pls solve neatly and faster thanks