Phase and Group Delays If the distortion is unacceptable, a delay equalizer is usually cascaded with the Lti system so that the overall group delay of the cascade is approximately linear over the band of interest To keep the magnitude response of the parent LTI system unchanged the equalizer must have a constant magnitude response at all frequencies Copyright C 2001, S K Mitra
Copyright © 2001, S. K. Mitra 16 Phase and Group Delays • If the distortion is unacceptable, a delay equalizer is usually cascaded with the LTI system so that the overall group delay of the cascade is approximately linear over the band of interest • To keep the magnitude response of the parent LTI system unchanged the equalizer must have a constant magnitude response at all frequencies
Phase and Group Delays Example- The phase function of the FiR filter yIn]=ax[n]+Bxn-1+ax[n-2 isθ(0)=-0 Hence its group delay is given by tg ()=1 verifying the result obtained earlier by simulation Copyright C 2001, S K Mitra
Copyright © 2001, S. K. Mitra 17 Phase and Group Delays • Example - The phase function of the FIR filter is • Hence its group delay is given by verifying the result obtained earlier by simulation y[n] = x[n]+ x[n −1]+ x[n − 2] () = − g () =1