The transfer function H(s) = 5+104 is proposed as a design for a high-pass filter (we shall later see in class what that means). (a) Show that this is a stable filter and determine its impulse response. (b) Determine the frequency response, H(w), of this filter. From this, determine the magnitude, H(w), of the frequency response as a function of frequency w (in radians). Also, determine the phase or angle, ZH(w), for the frequency response as a function of w. Note: H(W) = |HW|eiZHw) (c) The steady-state output signal (i. e. the limiting output as t + o) given the frequency response H(W) and input signal x(t) = A cos(wit+Pi) is given by Yss(t) = A|H(Wi) cos(wit+qi+ZH(Wi)). Determine the steady-state output signals of the filter to the following input signals. i. x(t) = 5 cos(100t + 7/8) ii. X(t) = 4 sin(1000t) iii. X(t) = cos(104) iv. x(t) = cos(10%t) V. X(t) = cos(106+)