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Identify whether the following system is minimum phase, maximum phase, mixed phase.$ (i) H_1(z)=6+ z^{-1} + z^{-2} (ii) H_2(z)=1 - z^{-1}- 6z^{-2} $
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written 7.5 years ago by | • modified 7.5 years ago |
$$a) H_1 (z) = 6 + z^{-1} - z^{-2} $$
$ H_1(z)=\dfrac {6z^2+z-1}{z^2}=\dfrac {6(z+1/2)(z-1/3)}{z^2}\\ zeros \space \space z_1=\dfrac {-1}2,z_2=\dfrac 13 $
As both zeros are inside unit circle, this system is minimum phase system.
$b) 1 -z^ {-1} -6z^{-2} \\ H_2(z)=1-z^{-1}-6z^{-2}\\ =\dfrac {z^2-z-6}{z^2}=\dfrac {(z+2)(z-2)}{z^2}\\ \text {zeros are at } z_1=-2, z_2=-3$
As both zeros are outside unit circle, this system is maximum phase system.