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3.5. Find mathematical expression of the following signals A(t) fa(t) fa(e) -2 4(t) fs(0) fat) 11...
3.5 Determine the output y(t) for the following pairs of input signals x(t) and impulse responses...
3.5 Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): 11) X (İİİ) x(1) = 11(1)-211(1-1) + 11(1-2), h(1) = 11(1 + 1)-11(t-1); Part lI Continuous-time signals and systems (iv) x(t) - e2"u(-t), h(t)-eu(); (v) x(t)-sin(2tt)(u(t _ 2) _ 11(1-5)), h (t) = 11(1) _ II(ț-2); (vi) x(t) = e-圳, h(t) = e-51,1. (vii) x(1)= sin(t)11(1), h(1) = cos(t)11(1).
3.5 Determine the output y(t) for the following pairs of input signals x(t) and...
Also : FS (2.8) FS (4) FS (5) The function f(t) is defined by -3t+6, 0<t<4...
Also :
FS (2.8)
FS (4)
FS (5)
The function f(t) is defined by -3t+6, 0<t<4 f(t) = -3, 4 < t < 5. Let f (t) denote the periodic extension of f(t), with period 5. Evaluate f (-2.3), f (O), f (7.5), f (9.2) and state the value to which the Fourier series of f (t), FS(t), converges for each of the following values: t = 0,t = 2.8, t = 4, t = 5. Enter all your answers...
2. Determine the FS coefficients for each of the following DT periodic signals. (a) x[n] =...
2. Determine the FS coefficients for each of the following DT periodic signals. (a) x[n] = sin(2 /3) cos(in/2) (b) x[n] periodic with period 4 and x[n] = 1 - sin n for 0 <n<3. (e) a[n) periodic with period 12 and [n] = 1 - sin for 0 <n<11.
2. a. Find the mathematical expression for the transient behavior of the voltage across the capacitor...
2. a. Find the mathematical expression for the transient behavior of the voltage across the capacitor of the following figure if the switch is thrown into position 1 at 0 s. 3 b. Repeat part (a) for ic c. Find the mathematical expressions for the response of ve and ic if the switch is thrown into position 2 at t 30 ms. d. 1.5 1.5 Find the mathematical expressions for the voltage vc and current ic if the switch is...
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...
Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana...
Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana -3т -2n -TT 2TT d) x(t) πι -no -TT 0 TE 2TT exponential FS f(t) = En=-- Cnejnwot Where (n = +S40+" f(t)e-inwot dt trigonometric 30 f(t)=a, + a, cos(no),t)+b, sin(no,t n-1 ao 1 T. 2 to a. So f(t)dt -5° f(t)cos(no),1)dt Sº f(t)sin(no,t)dt oy b 2 T
Find the trigonometric and exponential FS representations of the following periodic signals: a) 1 -20% 10%...
Find the trigonometric and exponential FS representations of the following periodic signals: a) 1 -20% 10% 20t -10 b) 1 TAJA. -/4 /4 -2 2R -I Verify that Parseval's Theorem holds for signal both sides of the following equation and verify that you get equality for case (a) above: a. That is, evaluate 4+7 1 To You may use MATLAB, calculator, etc. to approximately evaluate D(the larger 4+7 1 SxOf dt_ To the summation range, the better the approximation). Analytically...
Question (1) Find the Trigonometrie Fourier Series (FS) for the signals shown in Figure 1 and...
Question (1) Find the Trigonometrie Fourier Series (FS) for the signals shown in Figure 1 and Figure 2. M -6rt 41 -2 4r Figure 1 Figure 2 Question (2) (a) Find the power of x(t) = 5 + 10 cos (100t + 3) (b) Express signal x1(t) in terms of signal x(t) and its time-shifter, time-scaled, or time reversed versions. Figure 3
Find the trigonometric Fourier series (FS) and the exponential FS of the following: 2 *(1) 1.5...
Find the trigonometric Fourier series (FS) and the exponential FS of the following: 2 *(1) 1.5 1 0.5 O -0.5 1 -1 2 -1 0 2 b) 2 3 4 6 exponential FS Cnejnwot f(t) = En=-00 Where Cn 7Se+ f(t)e-inwot dt trigonometric f(t)= a, +Ža, cos(n6,t)+b, sin(n0,1 ao 1 T. 2 to an S f(t)dt sº f(t)cos(n0,1)dt f(t)sin (no,t)dt To 2 pt b,
1. If v(t)-40V at #300 and t 1ms, determine the mathematical expression for the sinusoidal voltage....
1. If v(t)-40V at #300 and t 1ms, determine the mathematical expression for the sinusoidal voltage. 2. A voltage expression is given as v, (t) -4 sin (2ot +50)V. Find its phase relationship with a, i(t) = 6 sin (20t + 40) b. v(t) 10 coS (20t 40) c. i(t) 3 sin (2ot 30) d. i(t)--3 cos (2ot + 90) 0??
3.5 Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): 11) X (İİİ) x(1) = 11(1)-211(1-1) + 11(1-2), h(1) = 11(1 + 1)-11(t-1); Part lI Continuous-time signals and systems (iv) x(t) - e2"u(-t), h(t)-eu(); (v) x(t)-sin(2tt)(u(t _ 2) _ 11(1-5)), h (t) = 11(1) _ II(ț-2); (vi) x(t) = e-圳, h(t) = e-51,1. (vii) x(1)= sin(t)11(1), h(1) = cos(t)11(1).
3.5 Determine the output y(t) for the following pairs of input signals x(t) and...
Also :
FS (2.8)
FS (4)
FS (5)
The function f(t) is defined by -3t+6, 0<t<4 f(t) = -3, 4 < t < 5. Let f (t) denote the periodic extension of f(t), with period 5. Evaluate f (-2.3), f (O), f (7.5), f (9.2) and state the value to which the Fourier series of f (t), FS(t), converges for each of the following values: t = 0,t = 2.8, t = 4, t = 5. Enter all your answers...
2. Determine the FS coefficients for each of the following DT periodic signals. (a) x[n] = sin(2 /3) cos(in/2) (b) x[n] periodic with period 4 and x[n] = 1 - sin n for 0 <n<3. (e) a[n) periodic with period 12 and [n] = 1 - sin for 0 <n<11.
2. a. Find the mathematical expression for the transient behavior of the voltage across the capacitor of the following figure if the switch is thrown into position 1 at 0 s. 3 b. Repeat part (a) for ic c. Find the mathematical expressions for the response of ve and ic if the switch is thrown into position 2 at t 30 ms. d. 1.5 1.5 Find the mathematical expressions for the voltage vc and current ic if the switch is...
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...
Find the trigonometric Fourier series (FS) and the exponential FS of the following: x(t) TT Ana -3т -2n -TT 2TT d) x(t) πι -no -TT 0 TE 2TT exponential FS f(t) = En=-- Cnejnwot Where (n = +S40+" f(t)e-inwot dt trigonometric 30 f(t)=a, + a, cos(no),t)+b, sin(no,t n-1 ao 1 T. 2 to a. So f(t)dt -5° f(t)cos(no),1)dt Sº f(t)sin(no,t)dt oy b 2 T
Find the trigonometric and exponential FS representations of the following periodic signals: a) 1 -20% 10% 20t -10 b) 1 TAJA. -/4 /4 -2 2R -I Verify that Parseval's Theorem holds for signal both sides of the following equation and verify that you get equality for case (a) above: a. That is, evaluate 4+7 1 To You may use MATLAB, calculator, etc. to approximately evaluate D(the larger 4+7 1 SxOf dt_ To the summation range, the better the approximation). Analytically...
Question (1) Find the Trigonometrie Fourier Series (FS) for the signals shown in Figure 1 and Figure 2. M -6rt 41 -2 4r Figure 1 Figure 2 Question (2) (a) Find the power of x(t) = 5 + 10 cos (100t + 3) (b) Express signal x1(t) in terms of signal x(t) and its time-shifter, time-scaled, or time reversed versions. Figure 3
Find the trigonometric Fourier series (FS) and the exponential FS of the following: 2 *(1) 1.5 1 0.5 O -0.5 1 -1 2 -1 0 2 b) 2 3 4 6 exponential FS Cnejnwot f(t) = En=-00 Where Cn 7Se+ f(t)e-inwot dt trigonometric f(t)= a, +Ža, cos(n6,t)+b, sin(n0,1 ao 1 T. 2 to an S f(t)dt sº f(t)cos(n0,1)dt f(t)sin (no,t)dt To 2 pt b,
1. If v(t)-40V at #300 and t 1ms, determine the mathematical expression for the sinusoidal voltage. 2. A voltage expression is given as v, (t) -4 sin (2ot +50)V. Find its phase relationship with a, i(t) = 6 sin (20t + 40) b. v(t) 10 coS (20t 40) c. i(t) 3 sin (2ot 30) d. i(t)--3 cos (2ot + 90) 0??
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