1. Consider the continuous-time system with the transfer function

H(s) = \frac{Ω_{0}^{2}}{s^{2} + \sqrt{2}Ω_{0}s + Ω_{0}^{2}}

with Ω_{0} = 2π(250).

(a) Is this a low-pass, high-pass, or band-pass filter?

(b) Use the method of impulse invariance to transform this filter into a discrete-time filter. Use a sampling frequency of 2 kHz. Plot the poles and zeros of the discrete-time filter using MATLAB’s zplane function.

(c) Plot the frequency response of the discrete-time filter (magnitude and phase). Does this look

like the type of filter you specified in Part (a)?

2. Repeat Problem 1 for the system with the transfer function

H(s) = \frac{s^{2}}{s^{2} + \sqrt{2}Ω_{0}s + Ω_{0}^{2}}

3. Problem 4.18

4. Problem 4.20

5. Probelm 4.24

6. Problem 4.36

7. Problem 4.44. Note that the input to the system should be r_{c}(t), not x[n].