As shown in the figures below,poles are distributed around z=1,similar to Butterworth designs,while zeros are arrayed on the unit circle at the stopband frequencies.Because zeros are not all located at z=-1,more multiplications are required in comparison to Chebyshev type I designs.OSB Example 7.5 compares Chebyshev type I and II filters in more detail. Chebyshev Type II Filter,7th Order Chebyshev Type II Filter,7th Order Pole-zero plot -1o4 号-204 -304 -40 -50 2 -1-0.5005 Impulse Response 4 34 2 34 20 30 Time,n Figre Magitude Plot,Detail,Group Deln 10:Pole-Zero Plot,Impulse Respon Design Specifications: Design Specifications nd edge =0.57. Passhand edge =0.5m. 2 Stopband edge =0.6. dann eage =0.0 gin =0 dB 二-30dB 5.Maximumn stopbsnd gain =-30 dB. In both of the Chebyshev design methods,having a monotonic behavior in either the passband or the stopband suggests a lower order system might exist such that it satisfies the given set of specifications,but varies with equal ripple in both the passband and the stopband. Elliptic Filters Four degrees of freedom:PB ripple,SB ripple,order,passband edge. Order of the system controls the transition bandwidth. Equiripple in both the passband and the stopband. Elliptic filters are the lowest order rational function approximation to a given set of magnitude specifications.All IIR filter designs we have discussed so far give nonlinear 7wn in the figures below, poles are distributed around z = 1, similar to Butterworth while zeros are arrayed on the unit circle at the stopband frequencies. Because are not all located at z = −1, more multiplications are required in comparison to yshev type I designs. OSB Example 7.5 compares Chebyshev type I and II filters in detail. • designs, zeros Cheb more As sho • In both of the Chebyshev design methods, having a monotonic behavior in either the passband or the stopband suggests a lower order system might exist such that it satisfies the given set of specifications, but varies with equal ripple in both the passband and the stopband. Elliptic Filters • Four degrees of freedom: PB ripple, SB ripple, order, passband edge. • Order of the system controls the transition bandwidth. • Equiripple in both the passband and the stopband. • Elliptic filters are the lowest order rational function approximation to a given set of magnitude specifications. All IIR filter designs we have discussed so far give nonlinear 7