Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

18-52 Passive, Active, and Digital Filters0−20−40−60−80−1000(a)0.2π 0.4π 0.6π 0.8π π0Amplitude in dB−20−40−60−80−1000(b)0−20−40−60−80−1000(c)0.2π 0.4π 0.6π 0.8π πLinear amplitude1.011.000.9900.025π0.2π 0.4π 0.6π 0.8π πFrequencyFIGURE 18.29 Typical amplitude responses for a filter of the form H(z) ¼ F(z L )G(z). L ¼ 8, v p ¼ 0.025p,v s ¼ 0.05p, d p ¼ 0.01, and d s ¼ 0.001. (a) F(z L ) of order 26 in z L . (b) G(z) of order 19. (c) Overall filter.For the order of F(z), a good estimate isN F F(d p, d s )=Lv s v p(18:95)so that it is 1=Lth of that of an optimum conventional nonperiodic filter meeting the given overall criteria.The order of G(z), in turn, can be estimated accurately by [10]231L=2whereN G ¼ cos h 1 (1=d s ) 4 X v p , 2p Lv pþ2v s3þ 5 (18:96a)X Lvp2 , p L(vpþ2vs)6X(v 1 , v 2 ) ¼ cos h 1 ½(2 cos v 1 cos v 2 þ 1)=(1 þ cos v 2 ) Š (18:96b)The minimization of the number of multipliers, [(N F þ 2)=2] þ [(N G þ 2)=2], with respect to L can beperformed conveniently by evaluating the sum of the above estimated orders for the admissible values of L,