Question

A minimum-phase continuous-time system has all its poles and zeros in the left-half s-plane. If a minimum-phase continuous-time system is transformed into a discrete-time system by bilinear transformation, is the resulting discrete-time system always minimum?

Answer 1

Yes

Explanation:

The statement given in question is true, a bilinear transformation will guarantee that a minimum phase discrete time filter is created from a minimum phase continuous time system

This is in accordance with that all poles and zeros in z -plane will be inside unit circle and hence the discrete time system has least phase angle. It is due to the fact that in bilinear transform maps a pole or zero at S0 to a pole of zero at Z0 plane,

S0 = a + j b

SInce all poles are in left, it means a < 0 , hence Z0 will be less than 1 also

Answer 2

Yes, a minimum phase continuous time system is also minimum phase when converted into discrete time system using bilinear transformation.

Explanation:

Bilinear Transform:

In digital signal processing, the bilinear transform is used to convert continuous time system into discrete time system representation.

Minimum-Phase:

We know that a system is considered to be minimum phase if the zeros are situated in the left half of the s-plane in continuous time system. In the same way, a system is minimum phase when its zeros are inside the unit circle of z-plane in discrete time system.

The bilinear transform is used to map the left half of the s-plane to the interior of the unit circle in the z-plane preserving the stability and minimum phase property of the system. Therefore, a minimum phase continuous time system is also minimum phase when converted into discrete time system using bilinear transformation.