Q1 In this question u(t) represents a unit step function, r(t) represents a unit ramp function and 8(t) represents a uni

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Q1 In This Question U T Represents A Unit Step Function R T Represents A Unit Ramp Function And 8 T Represents A Uni 1 (86.86 KiB) Viewed 21 times

Q1 In this question u(t) represents a unit step function, r(t) represents a unit ramp function and 8(t) represents a unit impulse function (a) Sketch the signals represented by the following functions. In each case use a time range of t = 0 to t = 10 seconds, and label appropriate points on the time and amplitude axes. (1) fi(t) = 5u(t) - 3ut - 4) - 2u(t-8) (4 marks) (ii) fz(t) = -2(t-1) + 4r(t - 3) - 2r(t - 6) - 2ut -9) (7 marks) (b) Evaluate the magnitude of the single impulse (sample) defined by each of the following functions: (1) f(t) = 8(t) x 5 cos(21 x 1000t) (3 marks) (ii) f4(t) = $(t - 4) xe -0.2t (3 marks) (c) Determine an expression using unit step functions u(t). and/or unit ramp functions r(t) as required, with appropriate scaling and shifting operations, to represent the signal x(t) shown in Figure Q1. X(t) (volts) 10.000 0.000 o doo 1.000 2.000 3.000 4.000 5.000 6.000 t(seconds) -10.000 Figure Q1 (8 marks)