Question

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|=1

The question was asked at a job interview.

Query is from Bilinear Transformations topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

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.