Design an analog low-pass filter satisfying the following magnitude specifications: max = 0.5 dB min

Design an analog low-pass filter satisfying the following magnitude specifications:

α_max = 0.5 dB                      α_min = 20 dB

Ω_p =1000 rad/sec             Ω_s =2000 rad/sec

(a) Use the Butterworth method. Plot the poles and zeros and the magnitude and phase of the designed filter. Verify by plotting the loss function that the specifications are satisfied.

(b) Use Chebyshev method (cheby1). Plot the poles and zeros and the magnitude and phase of the designed filter. Verify by plotting the loss function that the specifications are satisfied.

(c) Use the elliptic method. Plot the poles and zeros and the magnitude and phase of the designed filter. Verify by plotting the loss function that the specifications are satisfied.

(d) Compare the three filters and comment on their differences.