In bilinear transformation, the left-half s-plane is mapped to which of the following in the z-domain?(a) Entirely outside the unit circle |z|=1(b) Partially outside the unit circle |z|=1(c) Partially inside the unit circle |z|=1(d) Entirely inside the unit circle |z|=1The question was asked at a job interview.Query is from Bilinear Transformations topic in chapter Digital Filters Design of Digital Signal Processing

In bilinear transformation, the left-half s-plane is mapped to which o

1.	In bilinear transformation, the left-half s-plane is mapped to which of the following in the z-domain?(a) Entirely outside the unit circle \|z\|=1(b) Partially outside the unit circle \|z\|=1(c) Partially inside the unit circle \|z\|=1(d) Entirely inside the unit circle \|z\|=1The question was asked at a job interview.Query is from Bilinear Transformations topic in chapter Digital Filters Design of Digital Signal Processing
Answer» The correct option is (d) Entirely inside the unit circle \|z\|=1 Easy EXPLANATION: In BILINEAR transformation, the z to s transformation is given by the expression z=[1+(T/2)s]/[1-(T/2)s]. Thus unlike the backward difference method, the left-half s-plane is now MAPPED entirely inside the unit circle, \|z\|=1, rather than to a part of it.

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