2.从5)极点分布与原函数的对应关系 几种興型情况 S+a 2
2．H(s)极点分布与原函数的对应关系 j O −α α 0 jω 0 − jω 几种典型情况 p211 1 s 1 s a + 2 2 s + 2 1 s
Constraints of transformation In order to preserve the property of stability, If the continuous system has poles only in the left half of the s-plane then the discrete-time filter must have poles only inside the unit circle e m z plane Re Re
23 Constraints of Transformation ◆In order to preserve the property of stability, If the continuous system has poles only in the left half of the s-plane, then the discrete-time filter must have poles only inside the unit circle. s − plane Im Re Im z − plane Re
7. 1.1 Filter Design by Impulse Invariance The impulse response of discrete-time system is defined by sampling the impulse response of a continuous-time system n]=Thnt) Relationship of frequencies H(e)∑H!y+ 2丌 k=-∞ fH (Q)=0, l 27/Ta then H(em"=H j b bsm w=QT for y <丌
24 7.1.1 Filter Design by Impulse Invariance ◆The impulse response of discrete-time system is defined by sampling the impulse response of a continuous-time system. ( ) h n = Td hc nTd ( ) c Td if H j = 0, ( ) = w T w then H e H j d c j w , w= Td for w ( ) =− = + k d d c j w k T j T w H e H j Relationship of 2 frequencies
relation between frequencies Q=9,-x<O<丌,00<9<o Relationship of frequencies n(")=∑(1+1k H()=0.p2x“)=m上万 S plane 3/ Z plane
25 = Td ,− ,− relation between frequencies S plane Z plane - 3 / d T j / d T / d − T ( ) =− = + k d d c j w k T j T w H e H j Relationship of 2 frequencies ( ) c Td if H j = 0, ( ) = w T w then H e H j d c j w
No Aliasing in the Impulse Invariance H(e)=∑h1+ 2丌 k jH(A2)=0,g2≥7 k W then hle =h d 1≤丌 T H(e/ 26 2丌 2
26 No Aliasing in the Impulse Invariance ( ) =− = + k d d c j w k T j T w H e H j 2 ( ) c Td if H j = 0, ( ) , jw c d w then H e H j T w =