1. Find an expression for y[n] if y[n+ 2] + 2y[n+ 1]-8y[n] = r[n+2] - 2x[n+ 1] + 4r[n] with r[n] = (1.5)"u[n], y[−1] = −4, y[−2] = 4. The first few sub-questions below can be answered by just substituting values into the difference equation, but for the later ones you need to derive a general expression. (a) What is the value of y[0]? (b) What is the value of y[1]? (e) What is the value of y[2]?

1. Find an expression for y[n] if y[n+ 2] + 2y[n+ 1]-8y[n] = r[n+2] - 2x[n+ 1] + 4r[n] with r[n] = (1.5)"u[n], y[−1] = −4, y[−2] = 4. The first few sub-questions below can be answered by just substituting values into the difference equation, but for the later ones you need to derive a general expression. (a) What is the value of y[0]? (b) What is the value of y[1]? (e) What is the value of y[2]?

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

/ Determine Z-transform for the following sequences: a) x[n] = ()"(u[n] – u [n – 1]) %3D - b) x[n] = " cos () u[n]
Apply the convolution property of z-transform on given signals. x[n]="u[n] and y[n]=-u[n] b. Solve the given signal using properties of z-transform. x[n]=(){u[n] -u[n-8]} a. T
The inverse z-transform of F(z) is: 10z2 -42z z? –10z+21 F(z) = Select one: O a.f(k) = (3 × 3k) – (7 × 7') - O b. f(k) = (3 × 7k) + (7 × 3k) O c.f(k) = (3 × 3k) + (7 × 7k) O d. f(k) = (7 × 7k) – (3 × 3k)
3. Consider an LIT sysetm with input x[n] and output y[n] that satisfies the equation: 5 y[n] − zy[n − 1] + y[n − 2] = x[n] − x[n − 1] Please answer the following questions. You need to explain your answer in detail (a) How many possible ROC for z-transform in this system? (b) What is the possible values for the system's impulse response h[n] at n = 0 (i.e. h[0]) ?
3. Consider an LIT sysetm with input x[n] and output y[n] that satisfies the equation: 5 y[n] − zy[n − 1] + y[n − 2] = x[n] − x[n − 1] Please answer the following questions. You need to explain your answer in detail to get all score. (a) How many possible ROC for z-transform in this system? (b) What is the possible values for the system's impulse response h[n] at n = 0 (i.e. h[0]) ?
Q5: Find the Z-transform of the following: Hint: akf(k) = F (4) a) x(k) = 2k ek , b) x(k) = e-k sin wk , c) x(k) = 3-k sin wk %3D d) x(k) = 2k sin wk ,e)x(k) = ek sin wk , f)x(k) = ek k ak.
EXAMPLES: Z-TRANSFORM HW: x[n] = 28[n] + 38[n – 1]+ 58[n– 2]+ 28[n – 3]
2) x[n] can be decomposed as an infinite sum of U[n - k] as follows: r[n] = BiU[n – k]. k=-00 Find the coefficients Bk. Hint: Use the equality: d[n- k] = U[n - k] – U[n -k- 1].
Z-TRANSFORM SOLVE: yn+2 – 2 yn+1 + yn = 2n with y0 = 2, y1 = 1.
1- Find Z-transform if x(n) = blnl 2-If x(z) = 2z + 5z-1+ 6z-3 – z* find x(n). 3-Find zeros and poles of x(z): %3D (1--)(1-22-2) z + 2 4 – Find x(n) if x(z) : (z + 2)(z – 4) 5- If x(z) z-2 (2-z-2) find: %3! (a) [x(n) + x(n – 3)] * x(n) (b)x(n + 3) + 8(n – 1) 6- If x(n) = {2 1 -1 0 3},h(n) = {1 2 - 1}, Find out convolution of two sequences given above.
1. Explain in not less than 7 sentences with mathematical equations the relationship of z-transform and convolution sum. 2.Some transforms in the z-transform pairs are exactly the same. How would did they differ in other parts? What would be its implication when solving z-transforms?
3. Find the inverse z-transform of each of the following z-transforms. Determine the poles and zeros of each z-transform. a) X(z) = b) X(z) = c) X(z) = d) X(z) = 1-z-1 1-42-2 1-z-1 1-42-2 |z|>2 |z| 3 1 (1-32-1)2 12>2