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22 Transformation of Continuous-Time Signals Given the signals f), Jtt) and s(t) (quadratic piecewise functions) in...
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2, Ost<3 F(t) = {t + 4, 3 st<5 9, t25 [3 marks] ii. Use Laplace transforms to solve the initial value problem a) 7" + 16y = 4cos3t + s(t – 1/3) where y(0) = 0 and y'(0) = 0. [7 Marks) E.K. Donkoh (Ph.D) or [7 marks) B) y' – 3y = F(t), where y(0) = 0 and (sint, Osts F(t) = 1,...
(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...