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 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??