The magnitude frequency response for a network is sketched i

The magnitude frequency response for a network is sketched in below figure. The function H(s) is assumed to be rational. The sketch is not necessarily to scale, but the following specifics should be noted: |H(j omega)| is an even function of omega H(0) = 1 |H(f)| = 0 |H(j infinity)| = 0 In order to be compatible with the above data, what is the minimum number of zeros that H(s) can have? What is the minimum number of poles? Find an H(s) compatible with the above data. Suppose that the network function H(s) has minimum number of zeros and simple poles at s= -1, -1 plusminus j and no other poles. Suppose that the zero-state response \"y due to some input x and corresponding to high H(s) is y(t) = u(t)e^-t - u(t)e^-t cos t Find this input x(t)

Solution

a.

minimum number of zeroes for that function is 4,

h(jw)=(1-w)(1+w)(2+(1/w+1))(2-(1/w+1)).

minimum number of poles is 2.