Question 1: f(t) Complete the following parts for the signal f(t) shown in figure 1. Show complete work in (a, b) by constructing a table as discussed in lecture. (a) Write the mathematical expression for the signal f(t), using unit- step and ramp function. (b) Write the mathematical form of f(2-t/4) without plotting the Figure-1 signal. [Use property of unit step function] (c) Plot (i) f(-t)u(-1-t) (ii) f(t-2)[u(t) - u(t-4)] (iii) f(1-t)8(t - 1)Question 2: Find the fundamental period (T), fundamental frequency (f) and angular frequency (@) of the following signals, if the signal is periodic. (a) x(t) = cos(-) -5 sin( 5t 5t 2 ) + sin( 4 (b) x(t) = cos(3xt) + el(7/3), where j is an imaginary unit and j=-1 , elkl = coskt + jsinkt. 5 (c) x(t) = cos(-t) -5 sin( 3 7 t) + sin( 3 t)Question 3: Evaluate the following integrals using properties of impulse function: (a) [es/Cos(2' 8(1) dt , where j is an imaginary unit and j- =-1. (b ) [ ( 21 2 - 1)8 ( 21 + 3 ) dt -OC (c) [ sin( ! ) 8 (1 + 7 ) dt (d) [ sin( ! ) 8' (1 - 7 ) dt -00