A continuous-time linear time-invariant system is defined by the following transfer function H(s)=s2+4100s+(21000)2(21000)2 a) Calculate the poles and zeros for H(s). b) Based on the Nyquist sampling theorem, what is the suitable sampling frequency? c) If the sampling frequency is chosen at 4000Hz, calculate the transfer function H(z) for the equivalent discrete-time system using the poles of H(s) and the impulse invariant method. d) Repeat part c), but use the bilinear transformation method. e) Compare the frequency response of the discrete-time system H(ei2) obtained in part b) and c). [You may use MATLAB to solve this problem]