Impulse Invariant mapping [closed]

1. What are the limitations of impulse invariant mapping technique?
2. What is impulse invariant mapping?
3. Why impulse invariance method can not be used for high pass and band reject filter?
4. Why an impulse invariant transformation is not considered to be one to one?

What are the limitations of impulse invariant mapping technique?

The disadvantage of the impulse invariance method is the unavoidable frequency-domain aliasing.

What is impulse invariant mapping?

Impulse invariance is a technique for designing discrete-time infinite-impulse-response (IIR) filters from continuous-time filters in which the impulse response of the continuous-time system is sampled to produce the impulse response of the discrete-time system.

Why impulse invariance method can not be used for high pass and band reject filter?

The impulse invariance method is inappropriate for designing high-pass filters or stop-band filters due to spectrum aliasing that results from the sampling process.

Why an impulse invariant transformation is not considered to be one to one?

In Impulse Invariance there is "many to one mapping" and hence aliasing takes place. while in Bilinear Transform there is "one to one mapping" and hence no aliasing.