1. Determine Z-transform including region of convergencea) x(n)=n a" u(-n-1)b) x(n) = {1, 0, -1,0,1, -1)(G)" for n 2 0n for n<0c) x(n) =2. Compute the convolution of the following signalsfor n20andX1(n) =* for n<0(u)n O = (u) x3. Using long division, determine the inverse z-transform of1+ 2z-1X(z)1- 2z-1 + z-24. Determine the causal signal x(n) if its z-transform X(z) is given by:a) X(z) =1+3z-11+3z-1+2z-2b) X(z)1-r1+0.5z-2c) X(z) =2-15z-1%3D1-1.5z-1+0.5z-2z 6. Determine the response of the system with impulse response h(n)=a" u(n)to the input signal x(n)=u(n)-u(n-10).7. Let x(n) be a causal sequence with z-transform X(z) whose pole-zero plot isshown below. Sketch the pole-zero plots and the ROC of the followingsequence:Im[z)a) x1(n)=x(2-n)0.5b)x2(n)=e5* x(n)Re(z)-Oj50.5-0.58. We want to design a causal discrete-time LTI system with the property thatif the input is x(n) =;)" u(n) -)" u(n - 1)Then the output is y(n) = G)" u(n)Determine the impulse response h(n) and the system function H(z).9. Consider the causal systemy(n) = -a1y(n – 1) + box(n) + b,x(n- 1)Determine:(a) The impulse response(b) The step response(d) The response to the input x(n) = cos(won) 0sn

According to bartleby expert policy only one individual question with three subparts are to be…

Answered: 1. Determine Z-transform including…

1. Determine Z-transform including region of convergence a) x(n)=n a" u(-n-1) b) x(n) = {1, 0, -1,0,1, -1) G" for n 2 0 c) x(n) = for n<0 -n

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

9. Let f(r) = x[a.b) (x) be the characteristic function of the interval [a, b] c [-7, 7], that is, X[a.6) (2x) = { ! if x € [a, b], 0 otherwise. (a) Show that the Fourier series of ƒ is given by e-ina – e-inb „inz b - a f(r) ~ 27 2тin n#0 The sum extends over all positive and negative integers excluding 0. (b) Show that if a + –n or b# a and a + b, then the Fourier series does not converge absolutely for any r. [Hint: It suffices to prove that for many values of n one has | sin n6o| 2c> 0 where 09 = (b – a)/2.]
Q) find Fourier series on [-7,1] – 1 |4 -π
Determine Z-transform including region of convergence
Apply integration to the expansion 00 E(-1"x" = 1 – x +x² – x³ + ... 1+x n=0 to prove that for -1 < x < 1, (-1)"-!x" x2 x3 In(1 +x) = X -
n n x[n] = 7E" u[n] – 6)" u[n] Find the z-transform of the split-time signal below and show the Region of Convergence (ROC).
9. Let f(r) = x\a,b) (x) be the characteristic function of the interval [a, b] C [- π, π , that is { S1 if r€ [a,b], 0 otherwise. X[a,8)(x) (a Show that the Fourier series of ƒ is given by e-ina – e-inb einz b - a f(r) ~ 27 2тin The sum extends over all positive and negative integers excluding 0. (b) Show that if a + -r or b# n and a + b, then the Fourier series does not converge absolutely for any r. [Hint: It suffices to prove that for many values of n one has | sin n8o| 2c> 0 where 60 = (b – a)/2.] (c) However, prove that the Fourier series converges at every point r. What happens if a = -r and b= n?
Determine the z-transform of following sequences and state its region of convergence. i.) {(-3*} ii.) {cos kn} iii) iv.) {2e-3k + k2k-1}
Subject: calculus
3) x[n] = a"u[n] Prove that the z-transform of the equation is x(z) and plot the region of convergence. Z-a