Some examples of lower order Chebyshev polynomials are: 6(x)=1 Vi(z)=z V2(z)=cos(2 cos-1 z)=2cos2(cos-1x)-1=2x2-1 See Appendix B.2 of OSB for recurrence formulas for deriving Chebyshev polynomials. Equiripple in the passband,but decreases monotonically in the stopband. Similar to Butterworth filters,all zeros of a Chebyshev type I filter are located at z=-1. Following is a design example: Chebyshev Type I Filter,7th Order Chebyshev Type I Filter,7th Order Pole-zero plot 10 7产order29ro 0.5 兽-20 30 40 4 2 34 Frequency.m -10.5 Impulse Response 0.5 0.4 4 0.2 3/4 2 40 Time. Figre Magnitude Plot,Passband Detail,Group Delay :Pole-Ze Plot,Response n 2.Stopband edge =0.6m. 2 Stopband edre 3.Maximum passband gain =0 dB. 3.Maximum sshand gain =0 dB. 4.Minimum passband gain =-0.3 dB. 5.Maximum stopband gain =-30 dB. Type II 1 HCH(ejw)2= 1+(高号)厂 Monotonic in the passband;equiripple in the stopband. For a given set of specifications,the Chebyshev type I and Chebyshev type II design methods yield the same order. 6examples of lower order Chebyshev polynomials are: V0(x) = 1 V1(x) = x V2(x) = cos(2 cos−1 x) = 2 cos2(cos−1 x) − 1 = 2x2 − 1 Appendix B.2 of OSB for recurrence formulas for deriving Chebyshev polynomials. in the passband, but decreases monotonically in the stopband. to Butterworth filters, all zeros of a Chebyshev type I filter are located at z = −1. wing is a design example: Some Equiripple Similar Follo See • • Type II |HCH(ejω) 2 1 � tan (ω/2) ��−1 | = 1 + � �2V 2 N tan (ωc/2) • Monotonic in the passband; equiripple in the stopband. • For a given set of specifications, the Chebyshev type I and Chebyshev type II design methods yield the same order. 6