ANALYSIS+DESIGN OF LINEAR CIRCUITS(LL)
8th Edition
ISBN: 9781119235385
Author: Thomas
Publisher: WILEY
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Chapter 9, Problem 9.2P
To determine
The Laplace transform of
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- Find the z transforms of the following signs and draw the regions of convergence. In a. x[n] = n n-1 b. x[n] = ()" u[n – 4]arrow_forwardExpress the function below using window and step functions and compute its Laplace transform. 2190 Q 0- 5x 16 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t)= (sin 8t)u t-- (sin 8t)u (1-56) OB. 9(t)=11 sin (81) OC, 9(t) = (sin 8t)II 5x (t) + (sin 8t)u t- 0.7 16 salt) 0.16 I OD. g(t)=(cos 8t)u t-- : 8tu (1-556) 16 Compute the Laplace transform of g(t). L(g) = (Type an expression using s as the variable.)arrow_forward2. Find the z-transform of the following sequences: a. ak = cos(ak) b. bk = ak sin(bk) c. Ck = cos(ak) + sin(ak)arrow_forward
- What is the z-transform of:x(n) = 3nu(n-2)arrow_forwardQ1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n) d) 4(0.8) "cos (0.1лn)u(n) Q2 Given the two sequences x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4) a) Let x3(n) = x₁(n) * x2 (n) Determine the Z transform of x3(n) b) Find x3(n) using the inverse transform of X3(z). Q3 Using the Z-transform properties and the Z-transform table find the inverse Z- transform for each of the following sequences a) 5- (7z/z+1) - (3z/z-0.5) b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²] c) 3z/(z²+1.414z+1) d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75] Q4 Use partial fraction expansion, Find the inverse Z-transform of the following: a) [1/(z²+0.5z+0.06)] b) z/[(z+0.3)(z-0.5)] c) 5z/[(z-0.75) (z²-z+0.5)] d) 2z(z-0.4)/[(z-0.2)²(z+0.8)] Q5 A system is described by the following difference equation y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1) Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.arrow_forwardFind the z-transform X(z) of the signal x(n). Simplify the answer to only one rational term. Sketch/Draw the region of convergencearrow_forward
- From the first order system in the picture kv = 0.5 kp = 1.5 and ka = 4 using laplace transforms derive an expression to show how the output (angular displacement) will vary with time when a step input of 10v is appliedarrow_forwardSolve by Laplace transform method : x ’ = 2x – 2y y ’ = x – y – cos t x(0) = 3/5, y(0) = 4/5.arrow_forward2. Determine the inverse Z-Transform of the following signals. 5z а.x(2) — 3 + 2z (z – 2) (z – 0.3) 3z-1 b.x(z) (6z-2 – 5z-1 + 1)arrow_forward
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