6 Time and frequency characterization of s&s 6.2 The Magnitude-phase Representation of the frequency response of lti System System characterization Impulse response: h(t)F>H(o Frequency response H(@)= r(jo) X(o H(0)=H(o)e i∠H(O) IHG@- Magnitude response eJ2H(o Phase response
6 Time and frequency characterization of S&S 6.2 The Magnitude-phase Representation of the Frequency Response of LTI System System characterization: h(t) H( j) ⎯F → ( ) ( ) | ( )| j H j H j H j e = e Phase Response H j Magnitude Response j H j − − − − − − ( ) | ( )| Impulse response: ( ) ( ) ( ) X j Y j Frequency response: H j =
6 Time and frequency characterization of s&s 6.2.1 Linear and nonlinear phase Linear phase ∠H(jo)=ko Nonlinear phase: ZH(o)=Nonlinear function EXample: y(t=x(t-to) HGo=e oo HGo=-@to (Linear phase) Effect: Linear phase means non-distortion of signal transmission
6 Time and frequency characterization of S&S 6.2.1 Linear and Nonlinear Phase ( ) ( ) ( ) ( ) ( ) 0 0 0 H j t Linear phase H j e y t x t t j t = − = = − − Linear phase: H( j) = k Nonlinear phase: H( j) = Nonlinear function Example: Effect: Linear phase means non-distortion of signal transmission
6 Time and frequency characterization of s&s (Linear phase) Original signal Nonlinear phase
6 Time and frequency characterization of S&S ( Linear phase ) ( Nonlinear phase ) ( Original signal )