3.7. The input to a causal linear time-invariant system is x[n] = u[−n − 1] + (})" u[n]. The z-transform of the output of this system is Y(z) = (1 − −¹)(1 + z−¹)* (a) Determine H(z), the z-transform of the system impulse response. Be sure to specify the region of convergence. (b) What is the region of convergence for Y(z)? (c) Determine y[n].

3.7. The input to a causal linear time-invariant system is x[n] = u[−n − 1] + (})" u[n]. The z-transform of the output of this system is Y(z) = (1 − −¹)(1 + z−¹)* (a) Determine H(z), the z-transform of the system impulse response. Be sure to specify the region of convergence. (b) What is the region of convergence for Y(z)? (c) Determine y[n].

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

Similar questions

My question is under attachment.
Q1) Find the inverse z-transform f(n) for the following using long division method. 3z2(2z – 4) X(Z) : %3D (z – 2)(z – 0.7)(z – 1)
8) Determine the z-transform of the difference equation shown below. Do not simplify or solve for anything further. Just determine the z-transform. Assume that: • y(−1) = 10, y(−2) = 20 n • x(n) = (-)" u(n) y(n) + 1½y(n y(n)+y(n-2) = 8 x(n)
1. A function e(1) is sampled, and the resultant sequence has the z-transform z3 – 2z E(2): z* - 0.9z2 + 0.8 Solve this problem using E(2) and the properties of the -transform. a. Find the :-transform of e (t – 2T) u (1 – 27). b. Find the -transform of e (t +2) u(1). c. Find the z-transform of e (t -T) u (1 – 27).
Find the z-transform and its region of convergence (ROC) for each of the following sequences:..a) x[n] = δ[n]+δ[n-5]b) x[n]= (-0.5)nu[-n-1]
Description 1. Find the z-transform of each of the following sequences: (a) x(n) = u(n) – u(n-12) (b) x(n) = 6(n) + 36(n-1) + 26(n+3) (c) x(n) = (1/2)^u(-n)
Find Z-transforms and corresponding regions of convergence for the following signals:
Show me the steps of determine red
2- Find the z transform of the following two functions: (a) x₁(n) = n(0.5)"-2u(n) (b) x2 (n) = (0.5)"u(n-2)
1) Please solve the following difference equation for n ≥0. Solve this directly. Do not use z-transforms. y(n) - .7 y(n − 1) + .12 y(n − 2) = −75x(n) + 6.5(n − 1) where: x(n) 8(n); y(-1) = 100, y(-2) = 50, x(-1)=4;
4
1. Find the z-transform of the following signals: (a) a [n] = (-0.9)" u [n] (b) a [n] = (-0.9)"-'u [n – 1] (c) x [n] = -n (-0.9)" u [–n – (d) æ [n] = (-0.9)"-2 u [-n+ 1] + (0.8)"-lu [n – 1] (e) x [n] = (0.9)" cos (n) u [n] 2. Find the inverse z-transform of the following signals (a) X (2) = ; ROC = |2| > 1 (in closed form) +1: (b) X (z) = ; ROC = |2| > 1 (in power series form) (c) X (2) = , z3+1: ROC = |z| < 1 (in power series form) (d) X (z) = 23 –1 (z-0.5)²(z+1.5) ' ROC = (0.5 < |z| < 1.5) (in closed form) 3. x [n] = -6 [n + 2] + 28 [n + 1] + 8 [n] + & [n – 1] – 2 [n – 2] (a) Find the z-transform of x [n] (b) Find the z-transform of x [-n] (c) Find the Fourier-transform of x [n] (d) Find the Fourier-transform of x [-2n]