Question

Comparison between impulse invariance method and bilinear transformation

Answer 1

Impulse invariance method 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. The frequency response of the discrete-time system will be a sum of shifted copies of the frequency response of the continuous-time system.

The bilinear transformation method is an alternative to impulse invariance that uses a different mapping that maps the continuous-time system's frequency response, out to infinite frequency, into the range of frequencies up to the Nyquist frequency in the discrete-time case, as opposed to mapping frequencies linearly with circular overlap as impulse invariance does.

Answer 2

Impulse Invariance Method:

It is actually a technique in order to IIR or design  the discrete time infinite impulse response filters which use the continuous time system response in order to produce the pulse response. In other words it is actually a method of converting the analog function in to digital one. 

Bilinear transformation method:

It is actually the method which use the varying type of mapping which maps the  analog or the S plane in to the digital one. It actually transforms the filters of analog in to discrete equivalent using the  with the help of classical filter design techniques.