Problem 1. A Linear Time Invariant (LTI) system is defined by the Linear Difference Equation y[n]=1.2728y[n–1]-0.81y[n– 2]+x[n]– x[n– 1] with x[n], y[n] input and output sequences respectively. Q1. Determine its transfer function H(z),poles, zeros and Region of Convergence (ROC);

Problem 1. A Linear Time Invariant (LTI) system is defined by the Linear Difference Equation y[n]=1.2728y[n–1]-0.81y[n– 2]+x[n]– x[n– 1] with x[n], y[n] input and output sequences respectively. Q1. Determine its transfer function H(z),poles, zeros and Region of Convergence (ROC);

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 15EQ

See similar textbooks

Related questions

Q: For each of the ODEs in the 1st column, indicate whether it is: 1. linear time-invariant (LTI),…

A: A differential equation is said to be linear if every dependent variable and every derivative…

Q: 5. lim (* V1- t² dt) = X-1 (a) 3 (b) 2 (c) 1 (d) 0 6. If f(x) and g(x) are continuous functions at a…

A: our objective is to solve the problem

Q: 2. (LI-1) Compute the Wronskian for each set of functions below and determine whethe the set is…

Q: #6 Find the stability of the equilibrium value(s) from Problem #5. Graph the equilibrium (as a…

Q: Find the minimum value of q(x) = x" x subject to the condition ||x|| = 1. %3D Select one: O A. 2 -…

Q: 3. Let f(t) be the function graphed below. Let g(x) = ƒ f(t)dt -0:8 -0:6 -0:4 -0.2 0,5 15 2.5 -0:2…

Q: 1. Let u = f+cK* u with c real and K(x) = H(x)be-ba, b>0. (a) Find the general solution. (b) For…

A: As per the question we are given the following equation : u = f + cK * u Where K(x) = H(x)be-bx ,…

Q: (7) Find the local linear approximation of f(x) = √2+3 at zo = and use it to estimate the val of…

A: The linear approximation of function f(x) at is The given function is

Q: 5.3. Consider the quadratic function f (x) = x"Qx -c'x, where Q is a positive-definite matrix. Let p…

A: Given- Consider the quadratic function fx = 12xTQx - cTx, where Q is a positive-definite matrix. Let…

Q: 4) Consider the equation (2x? – 3x – 8)y" + 4xy' – y = 0. A solution to this equation is y(x) = > bn…

A: Given the differential equation, 2x2-3x-8y''+4xy'-y=0 ⋯⋯(1) Which is in the form,…

Q: 1. Show that va(z(t), t) = z(t)P"(t)Q(t)P(t)z(t) is a Lyapunov function that proves uniform…

A: Sol

Q: (a) Consider the additive model Xt = m + Yt with cubic trend mt= Bo + B₁t+ ß₂t² + B3t³. (i) Show…

A: Given Information: a) Additive model Xt=mt+Yt with mt=β0+β1t+β2t2+β3t3. To show: i) ∇mt is the…

Q: Y(s) For the following transfer function, = F(s) where U(s) = U (s) erive the time function y(t).…

A: We have

Q: (b) Write the following boundary value problem as a system of first order odes. u" +3u' = 0, for tE…

A: given system of first order u''+3u'=0 for t∈0,1 with boundary conditions u0=1 , u'1=sinu0 write the…

Q: Solve the following LPP using Big M-Method. Max P = 3x1 - 2x2 Subject to 2x1 + x2 ≥ 3 x1 + 2x2 ≤ 2…

A: The given problem is to solve the given linear programming problem with given constraints by using…

Q: problem (A), find a linear approximation f(x, y) at the indicated point. [3x – y² A) f(x,y) = at…

A: .

Q: 3.13 Consider the system * = 4x²y-f(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous…

A: Given the autonormous non-linear system, x˙=4x2y-f1xx2+2y2-4 1y˙=-2x3-f2yx2+2y2-4…

Q: A process described by the transfer function (10s+1) G,(S) = (5s+1) is forced by a unit step input…

Q: Problem Consider the following optimization problem: min f(x, y) = 3x? + y* x,y (a). Apply one…

A: The question is based on the subject computer science.

Q: 4. The weekly demand for the Pulsa 25 color LED television is p= 600– 0.05x (0<p<12000) Where p is a…

A: Given

Q: Problem Consider the following optimization problem: min f(x, y) = 3x² + y² x,y (a). Apply one…

A: The given optimization problem: min f(x, y) = 3x²+y¹ We have to Apply one iteration of the gradient…

Q: Determine the poles and zeros of the transfer function: Select one: O A. poles: 0, -2, -5 + j10;…

A: We have to find the poles and zeros of transfer function 40(s+2)(s2+10s+125)

Q: Consider the two-step difference scheme w;-1 = -4w, + 5u,-1 + 4hf(t;, w) + 2hf(t,-1, ;-1) for…

A: Consider the equation

Q: (c) Suppose that only two firms supply the market and each firm chooses its output in period t + 1…

A: Differential equations Advance maths

Q: 7. The final value for the function [ f(s) = (75s+84)/(15s²+ 21s)] is:- a. 5 b. 28/5 c. 25/7 d. 4

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 7:31 MAC2311C-FINAL-A PDF - 234 KB 4 Problem 4. Using Table 1 reproduced below for cordiality, 34 5…

A: For maxima/minima of f(x): f'(x) = 0 From table f'(x) = 0 at x = 4

Q: s(s² +95+19) B) Determine the response of the following closed loop transfer function for unit step…

Q: 11. Show that the generating function Hn of the total number of individuals in the first n…

Q: Suppose f(): R" → R is a function. Consider the optimization problem min f(x) over XER". P) 3)…

A: Given: A function . Consider the optimization problem min over Aim: If , What is the second-order…

Q: The following transfer function is not written in a standard form: 2(s + 0.5) G(s) = (s + 2)(2s + 1)…

A: The transfer function is as follows:To Find:a) Put it in standard form.b) Gain, poles, and zeroes.c)…

Q: 26. A polynomial P(x) has a relative maximum at (-2,4), a relative minimum at (1,1), a relative…

A: Given The polynomial relative maximum at (-2,4), (5,7) and relative minimum at (1,1) .

Q: 3) The transfer function of a control system is given by G(s) = 25/ (s + 6s + 25). The first maximum…

A: Given: G(s)=25s2+6s+25 The standard equation is, G(s)=Kwn2s2+2wnδs+wn2 Compare the standard equation…

Q: For an M/M/1 queueing system, L =λ/(μ - l). Suppose that λ and μ are both doubled. How does L…

A: Given information: For a M/M/1 queueing system, the λ and μ are both doubled.

Question

**Problem 1.** A Linear Time Invariant (LTI) system is defined by the Linear Difference Equation

\[ y[n] = 1.2728y[n - 1] - 0.81y[n - 2] + x[n] - x[n - 1] \]

with $ x[n], y[n] $ input and output sequences respectively.

**Q1.** Determine its transfer function $ H(z) $, poles, zeros, and Region of Convergence (ROC).

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fourier Transformation$

Learn more about

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

Similar questions

9) Find a linear function of the form f(x) = ax +b that satisfy the conditions A-4) = 8 and (3) - 9.
The value of Wronskian of two functions y, =7* and y, =7** is =7*+4
(2) The annual net profit for a company, from 1995 to 2005, can be approximated by the model an 10e0.2n, n = 1, 2, 3, ., N, where an is the annual net profit in millions of dollars, and n represents the year, with n =1 corresponding to 1995. Estimate the total net profit during this period. (3) A deposit of 15 dollars is made at the beginning of each month, for a period of 5 years, in an account that pays 0.9 % interest, compounded monthly. Find the balance in the account at the end of the 5 years. (4) A deposit of 20 dollars is made every 3 months, for a period of 10 years, in an account that pays 1% interest, compounded quarterly. Find the balance in the account at the end of the 10 years. (5) A deposit of $500 can be made with two options: earn 2% interest, compounded quarterly for 3 years, or earn 1.5%, compounded monthly for 3 years. Find the balance after 3 years of both options.
Scenario You are employed as a network engineer and have been asked to analyze a Sender A () в () Receiver communication network to determine the current data rates and ensure that 100 X2 the links aren't at risk of "reaching capacity." In the following figure of the E () network, the sender is transmitting data at a total rate of 100+50 = 150 megabits per second (Mbps). The data is transmitted from the sender to the C (). D (). 120 ...- receiver over a network of five different routers. These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as X1, X2, X3, X4, and X5.
Determine y'of (3x + 1)ª(2x – 1)³
3) f(x)=x²-5x-6 4 1 4) f(x)= x³ x³ (ans.: max.(-1,-2); min.(1,-10)) (ans.: min.(0.25,-0.47 ))
Is the set of functions f₁(x) = ex · f₂(x) = ex- linearly dependent or linearly independent on (-∞, ∞)? Discuss. Since e -6 e ex + 4, we see that e* is a constant multiple of e* + 4 and the set of functions is linearly dependent ×
PO' (14) Find two different reduced systems of residues modulo 8.
Find the derivative of 3 -8-5-5 6 -2 0 5-5 1 fx) = det-1 0 0 -2 8 %3 x -6-9 1 1 -3 6 00 0-4 0 0 OA-(-3)(5)(-2)(-4) O B. - (-8)(5)(-2)(-4) OC-(-3)(2)(-2)(-4) O D.-(-3)(5)(-2)(-4) OE. E(-8)(5)(-2)(-4)
Ive the system by using the inverse o A^(-1)=[[-(92)/(289),(58)/(289),-(45)/(289),(5)/(289),(31)/(289),(27)/(289),-(6)/(289)]] (7)/(289) (12)/(289) -3x-3y+7z=70 x+3y+8z=51 x+10y-4z=-26 No hand written and fast answer with explanation
2. Start: y= x End: y =)' +5 -9(x-8 What transformations occurred?
If y=u³-4 and u = 3x² + 10, find y' O 18x(3x² + 10)² O 3x(6x² + 10)² 18(3x² + 10)² O 6x(3x² +10)² Moving