Chapter 5 Transform Analysis of inear Time-Invariant systems ◆50 Introduction 5. 1 Frequency Response of LTI Systems 5.2 System Functions For Systems characterized by linear Constant-coefficient Difference equation 5.3 Frequency response for rational system Functions 5.4 Relationship Between Magnitude and phase ◆5.5A- Pass system 5.6 Minimum-Phase systems 5.7 Linear Systems with generalized linear phase
2 Chapter 5 Transform Analysis of Linear Time-Invariant Systems ◆5.0 Introduction ◆5.1 Frequency Response of LTI Systems ◆5.2 System Functions For Systems Characterized by Linear Constant-coefficient Difference equation ◆5.3 Frequency Response for Rational System Functions ◆5.4 Relationship Between Magnitude and Phase ◆5.5 All-Pass System ◆5.6 Minimum-Phase Systems ◆5.7 Linear Systems with Generalized Linear Phase
5.iNtroduction An LTI system can be characterized in time domain by impulse response hn] Output of the Lti system ]=x*=∑xk-k] With Fourier transform and z-transform an LTI system can be characterized Cin Z-domain by system function H(z) Y(z)=H()x()y(e")=h(e)x(e") Cin frequency-domain by Frequency response H
3 5.0 Introduction ◆An LTI system can be characterized in time domain by impulse response ◆Output of the LTI system: h n =− = = − k y n x n h n x k h n k Y(z) = H(z)X(z) ◆in Z-domain by system function ◆in frequency-domain by Frequency response ( ) ( ) ( ) j w j w j w Y e = H e X e ◆With Fourier Transform and Z-transform, an LTI system can be characterized H z( ) ( ) jw H e
5.1 Frequency Response of LTT Systems Frequency response hle/ Useful input signal Yle/=hle/wintel deleterious signa ◆ Magnitude response(gain)Hle") change on to Y(en)=H(emx(ery useful signal distortions . Phase response(phase shift)H(e/") ∠y()=∠H(e")+∠x(em)
4 5.1 Frequency Response of LTI Systems ( ) ( ) ( ) j w j w j w Y e = H e X e ( ) ( ) ( ) j w j w j w Y e = H e X e ◆Phase response (phase shift) ( ) jw H e ( ) ( ) ( ) j w j w j w Y e = H e +X e ( ) jw ◆Frequency response H e ( ) jw ◆Magnitude response (gain) H e distortions change on useful signal system Useful input signal + deleterious signal
5.1.1 Ideal Frequency-Selective Filters ◆ Ideal lowpass filter 少<W e -0<n<O ◆ Noncausal,not computationally H realizable ◆ no phase distortion 2丌 丌-W W,丌 2丌 C C
5 5.1.1 Ideal Frequency-Selective Filters ◆Ideal lowpass filter ( ) 1, 0, jw c lp c w w H e w w = ( ) jw H e 0 − 2 − − wc wc 2 1 sin , = − c lp w n n h n n ◆Noncausal, not computationally realizable ◆no phase distortion
5.1.1 Ideal Frequency-Selective Filters ◆ Ideal highpass filter 1-H(e)=b(a") 0 <W v<w|≤丌 sin w n n=on 0<n<0 元n H 2丌 2丌 6
6 5.1.1 Ideal Frequency-Selective Filters ◆Ideal highpass filter ( ) 0, 1, jw c hp c w w H e w w = sin , c hp w n h n n n n = − − − 2 − − wc 0 wc 2 ( ) jw H e 1 1 ( ) jw − H e lp =