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find the z transform (c) f(x)=(0.5)* cos( * ), (2-2) (d) f(k)=[(0.2)* +(-2)*-*]u. (k).
a)
b)
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0.5 F + 0.2 VX 20 u(t) Ve 1H CHAPTER 12 – Introduction to the Laplace Transform K* ) Let F(s) = (sta-ikir + istati jr, K = \Kleje. K i. Prove that the inverse Laplace transform of F(s) is, [2lkone-at cos(ßt + 0)]u(t). Find f(t) if F(s) = 25s2 + 395s + 1494 s2 + 15s + 54
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
3. The signal x[n] =-(b)”u[-n – 1]+ (0.5)”u[n], a) find the z-transform X(z) [5] b) plot the ROC. [3] С
(a) Find the z-transform of (i) x[n] = a"u[n] +b"u[n] + cºul-n – 1], lal <151 < le|| (ii) x[n] = n*a"u[n] (iii) x[n] = en* [cos (în)]u[n] – en" (cos (ien)] u[n – 1] (b) 1. Find the inverse z-transform of 1-jz-1 X(2) = (1+{z-1)(1 – {z-1) 2. Determine the inverse z-transform of x[n] is causal X(x) = log(1 – 2z), by (a) using the power series log(1 – x) = - 95 121 <1; (b) first differentiating X(2)...
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3" n] 0.5" cos (10n)u[n] In]-(0.3) u[/n] The transfer function of a discrete time system is H(z)- 20. 1+2z3z Use the inverse Z-transform to determine the system difference equation [4 Marks] 21. An LTI system is described by the following input/output difference equation: yln] 0.12yln x[n] (assume zero initial...
Question 2: Find the inverse z-transform of the following functions: z-'(0.5- 2*') by F(z)= (1 -0.5z"')(1 – z')? b F_(7) = (0.5 – 2 ')(1+1.37" +0.42%) O F(2) = 1+6z2+z? (1 - z ')(1 -0.25z') (1 - z- ')(1-0.5z') 0.368z+0.478z+0.154 e) F(z) = 0 (z-0.6)z? f) F (Z) = - Z? - 7z+12
(a) Find the z-transform of (i) x[n] = a"u[n] + B^u[n] + cºul-n – 1], lal< 161 < le| (ii) x[n] = n-au[n (iii) x[n] = {** [cos (Tan)]u[n] -em* [cos (fin)]u[n – 1]
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10.33 Inverse Z-transform- Use symbolic MATLAB to find the inverse Z-transform of 2 -z 21 +0.25z(i +0.5z1 and determine x[n] as n → oo. 1080 Answers: xfn] = [-3(-0.25)" + 4(-0.5)"]u[n]
10.33 Inverse Z-transform- Use symbolic MATLAB to find the inverse Z-transform of 2 -z 21 +0.25z(i +0.5z1 and determine x[n] as n → oo. 1080 Answers: xfn] = [-3(-0.25)" + 4(-0.5)"]u[n]
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier series: i) 2
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2