No Aliasing in the Impulse Invariance 2丌 H()=0.12z/,hn(")=H/yr No Aliasing
29 No Aliasing in the Impulse Invariance ( ) =− = + k d d c j w k T j T w H e H j 2 − ( ) 0, , c d if H j T = ( ) , jw c d w th n H e H j T e w = No Aliasing
Aliasing in the Impulse Invariance p(")=∑ 2丌 H+17k,扩(19)≠0,2≥x/ k: henH(e")≠Ha(T) Aliasing ≤丌 2 7/T AT 27/ Td 2丌
30 − Td Td − Aliasing in the Impulse Invariance ( ) 2 , jw c k d d w H e H j j k T T =− = + ( ) 0, , c d if H j T ( ) , jw c d w th n H e H j T e w − 2− Td 2 Td Aliasing
Steps of DT filter design by transforming a prototype continuous-time filter ◆① Obtain the specifications for continuous time filter by transforming the specifications for the desired discrete-time filter ◆② Find the system function of the continuous- time filter ◆③ Transform the continuous-time filter to derive the system function of the discrete time filter 31
31 Steps of DT filter design by transforming a prototype continuous-time filter ◆① Obtain the specifications for continuoustime filter by transforming the specifications for the desired discrete-time filter. ◆② Find the system function of the continuous- time filter. ◆③ Transform the continuous-time filter to derive the system function of the discretetime filter
(1 Transformation of specifications from discrete to continuous In impulse invariance design procedure assuming the aliasing in transformation is neglected, relation of specifications n transformation is H(n)=B()H(1)=H(e0) O≤丌 Passband Transition Stopband P 0 S 32
32 ① Transformation of specifications from discrete to continuous ◆In impulse invariance design procedure, assuming the aliasing in transformation is neglected, = Td p p d s s d T T = = relation of specifications in transformation is Td =( ) ( ), j H j H e c c ( ) = ( ) H j j H e
Steps of DT filter design by transforming a prototype continuous-time filter ◆① obtain the specifications for continuous time filter by transforming the specifications for the desired discrete-time filter ◆② Find the system function of the continuous-time filter ◆③ Transform the continuous time filter to derive the system function of the discrete time filter 33
33 Steps of DT filter design by transforming a prototype continuous-time filter ◆① Obtain the specifications for continuoustime filter by transforming the specifications for the desired discrete-time filter. ◆② Find the system function of the continuous-time filter. ◆③ Transform the continuous-time filter to derive the system function of the discretetime filter