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6. Determine the T anlace transform of graph shown. The graph is dis h , at...
Solve for lapalce transform. 3. For the RLC circuit shown in the graph, determine the current...
Solve for lapalce transform.
3. For the RLC circuit shown in the graph, determine the current i (t), taking into account that. i(0) = 0 y 9(0) = 0 L = 1 h, R = 1602, C = 10-4f, E = 20v 00000 L E R
Question 4 (a) Determine the Fourier transform of v(t) in the circuit shown in Figure 4...
Question 4 (a) Determine the Fourier transform of v(t) in the circuit shown in Figure 4 below. (10 marks) 232 e-21u(t) V (+ + v(t) + IF ele 0.5H 28(1) A Figure 4 (b) For the network shown in Figure 5, by means of the Laplace Transform, evaluate i(t). (15 marks) 2e-fu(t) V + 1F io 1 H HI 112 WW 4u(t) A 122 Figure 5
Find the inverse Fourier Transform of H(jω) shown below: 6(3+j2w) H(W) = (1 + iw)(4 +...
Find the inverse Fourier Transform of H(jω) shown below:
6(3+j2w) H(W) = (1 + iw)(4 + jw)(2 + jw) Answer: h(t) = (2e-+ 3e-2t – 5e-4t)u(t)
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
1. Determine the Laplace transform of the following signals e* .11(t) ; (b) g(t)=Icos(2) + sin(2t)j.u(1-3)...
1. Determine the Laplace transform of the following signals e* .11(t) ; (b) g(t)=Icos(2) + sin(2t)j.u(1-3) ; (c) h(t)-t-e-21. cos(30.11(1) 2. Determine the Laplace transform of the non-periodic signal shown below: h(t) 0 1 2 3 4 t 3. Determine the Laplace transform of the periodic waveforms shown below: fa) f(t) 0 2T 4T 6T 8T 4. Determine the inverse Laplace transform of the following signals 2s (b) G)6s+12 H(s) =s.(14%) (a) F(s)-De (c) (2s +1)(s1 +5s +6 5. Using...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
Sketch the graph of the function below and determine its Laplace transform. uſt-6) -ut-10) Click here...
Sketch the graph of the function below and determine its Laplace transform. uſt-6) -ut-10) Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms. Sketch the function's graph. Choose the correct answer below. OA Oc OD A910 OB Agro 3 910 4910 3 @ O 0 12 OP Determine the Laplace transform zut-6) - u-101-0 Express the function below using window and step functions and compute its Laplace transform. Ag(t)...
For the graph y = p(t) shown to the right, determine the points of discontinuity and...
For the graph y = p(t) shown to the right, determine the points of discontinuity and justify your answer. 1pt) 10 6 0 2 و لا 4 6
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of...
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of the Laplace Transform to show that -5s 3. Find the inverse Laplace transform of the following: (a) T(s)-( (b) Y(s)=式 ) (劫 +3s 4. Solve the the following initial value problem: Sketch the function, f(), and the solution vit) on the same graph. 5. Solve the the following initial value problem: y" + 144y = δ(t); y(0) = 0, ช่ (0) =0
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) =...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Solve for lapalce transform.
3. For the RLC circuit shown in the graph, determine the current i (t), taking into account that. i(0) = 0 y 9(0) = 0 L = 1 h, R = 1602, C = 10-4f, E = 20v 00000 L E R
Question 4 (a) Determine the Fourier transform of v(t) in the circuit shown in Figure 4 below. (10 marks) 232 e-21u(t) V (+ + v(t) + IF ele 0.5H 28(1) A Figure 4 (b) For the network shown in Figure 5, by means of the Laplace Transform, evaluate i(t). (15 marks) 2e-fu(t) V + 1F io 1 H HI 112 WW 4u(t) A 122 Figure 5
Find the inverse Fourier Transform of H(jω) shown below:
6(3+j2w) H(W) = (1 + iw)(4 + jw)(2 + jw) Answer: h(t) = (2e-+ 3e-2t – 5e-4t)u(t)
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
1. Determine the Laplace transform of the following signals e* .11(t) ; (b) g(t)=Icos(2) + sin(2t)j.u(1-3) ; (c) h(t)-t-e-21. cos(30.11(1) 2. Determine the Laplace transform of the non-periodic signal shown below: h(t) 0 1 2 3 4 t 3. Determine the Laplace transform of the periodic waveforms shown below: fa) f(t) 0 2T 4T 6T 8T 4. Determine the inverse Laplace transform of the following signals 2s (b) G)6s+12 H(s) =s.(14%) (a) F(s)-De (c) (2s +1)(s1 +5s +6 5. Using...
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
Sketch the graph of the function below and determine its Laplace transform. uſt-6) -ut-10) Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms. Sketch the function's graph. Choose the correct answer below. OA Oc OD A910 OB Agro 3 910 4910 3 @ O 0 12 OP Determine the Laplace transform zut-6) - u-101-0 Express the function below using window and step functions and compute its Laplace transform. Ag(t)...
For the graph y = p(t) shown to the right, determine the points of discontinuity and justify your answer. 1pt) 10 6 0 2 و لا 4 6
1. Sketch a graph of the following function: f(t)-5(H(t) -2H(t-1)+ H(t-2)) 2. Use the definiton of the Laplace Transform to show that -5s 3. Find the inverse Laplace transform of the following: (a) T(s)-( (b) Y(s)=式 ) (劫 +3s 4. Solve the the following initial value problem: Sketch the function, f(), and the solution vit) on the same graph. 5. Solve the the following initial value problem: y" + 144y = δ(t); y(0) = 0, ช่ (0) =0
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
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