Example 5.1 Effect of Attenuation and Group Delay 0.85兀w=0.25msm 0.5 =0.5兀 连贯的 Three consecutive narrowband pulses 200 Sample number (a is applied to'a filter urig Transform Magnitude of Input x[n 15 u10 0.20.4 0,6D.8 12m1.41.6 1.8 2 Radian frequency (an) (b) 12
12 w= 0.85 w= 0.25 w= 0.5 Example 5.1 Effect of Attenuation and Group Delay Three consecutive narrowband pulses is applied to a filter 连贯的
Ex, 5.1 Effect of Attenuation and Group delay Filter frequency response Group Delay 200 Group Delay 150 100 50 0.2 0.4 0.6丌0.8 12 1.4 1.6 1.8 W=0.25 Radlan frequency (to) Frequency Response Magnitude =0.5丌 =0.857 100 magnitude 200 0.2m0.4W0.6丌0.8 1.2714丌1.6丌1.8m 2丌 Radian frequency(a)
13 Ex. 5.1 Effect of Attenuation and Group Delay Filter frequency response Group Delay magnitude w= 0.25 w= 0.85 w= 0.5
Input Signal x[nl 0.5 三0 0.5 Group Delay 100 150 200 25200300 3 400 Samile nun v=0.85丌 =0.5丌 W=0.25 Output Signal yInI Group Delay 0.5 50 W 0.5 0 0 150 200 250 300 35 400 Sample number(n) 14
14 w= 0.85 w= 0.5 w= 0.25 Group Delay 50 Group Delay 200
2 Phase Distortion and Delay delay distortion is a rather mild form of phase distortion, its effect is to shift the sequence in time we accept linear phase response rather than zero phase response Ideal lowpass filter with linear phase delay Ww H 0,w<w≤丌 CThe impulse response(delayed by time nd) hin(n) sm wcn-nd X<1<∝ n(n-nd
15 5.1.2 Phase Distortion and Delay ◆Ideal lowpass filter with linear phase delay ( ) , 0, d jwn jw c lp c e w w H e w w − = ( ) ( ) ( ) − − − = n n n n w n n h n d c d l p , sin ◆delay distortion is a rather mild form of phase distortion, its effect is to shift the sequence in time. we accept linear phase response rather than zero phase response. ◆The impulse response (delayed by time nd )
5.2 System Functions For LTI Systems Characterized by Linear Constant coefficient Difference equation K Linear Constant-coefficient difference equation ∑ayln-k]=∑bxm-k k=0 k=0 k 人力 y(z)=∑bzX(z) k=0 ∑azk|y(z)=∑bzkx() k=0 k=0
16 5.2 System Functions For LTI Systems Characterized by Linear Constantcoefficient Difference equation ◆Linear Constant-coefficient Difference equation = = − = − M k k N k k a y n k b x n k 0 0 ( ) ( ) = − = − = M k k k N k k k a z Y z b z X z 0 0 a z Y(z) b z X (z) M k k k N k k k = = − = − 0 0