The MATLAB signal processing toolbox function ellip helps design digital elliptic filters. An elliptic filter has ripple in both the pass band and the stop band. Setting the pass band ripple to R_{p}=3 dB and the stop band ripple R_{s}=20 dB down, repeat Prob. 5.M-8 using the ellip command.

Problem 5.M-8

The MATLAB signal processing toolbox function butter helps design digital Butterworth filters. Use MATLAB help to learn how butter works. For each of the following cases, design the filter, plot the filter's poles and zeros in the complex z plane, and plot the decibel magnitude response 20 log10 |H(e^{Ω})|.

a. Design an eighth-order digital low pass filter with Ω_{c} = π/3.

b. Design an eighth-order digital high pass filter with Ω_{c} = π/3.

c. Design an eighth-order digital band pass filter with pass band between 5π/24 and 11π/24.

d. Design an eighth-order digital band stop filter with stop band between 5π/24 and 11π/24.