Question

In the Bilinear Transformation mapping, which of the following are correct?

(a) All points in the LHP of s are mapped inside the unit circle in the z-plane

(b) All points in the RHP of s are mapped outside the unit circle in the z-plane

(c) All points in the LHP & RHP of s are mapped inside & outside the unit circle in the z-plane

(d) None of the mentioned

I got this question in quiz.

The above asked question is from IIR Filter Design by the Bilinear Transformation topic in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct choice is (c) All points in the LHP & RHP of s are mapped inside & outside the unit circle in the z-plane

Explanation: The bilinear transformation is a conformal mapping that transforms the jΩ-axis into the unit circle in the z-plane and all the points are linked as mentioned above.