Given that the system function of a third order Butterworth type analog low-pass filter with a 3 dB cut-off frequency of 2 radian/second is: 2s HS = S2 + 0.2 s +1
Answer the following questions:
1. Use the bilinear transformation to obtain H(z). Use T=2 second.
2. Give H(w) for your filter.
3. Use MATLAB to give the magnitude spectrum.
4. Comment on the quality of the design.
5. With the aid of simple sketch graphs explain how frequency warping affects the frequency response of the digital filter.
6. Comment on the need for prewarping, i. e. give conditions when prewarping is needed.