We have studied six methods for approximating an analog filter by an IIR digital filter.  Impulse Invariant, Step Invariant, Finite Difference, Matched-z, Direct Substitution and Bilinear

(a) Which method(s) can be done without using any time-domain functions in the process?

(b) Which method(s) squeeze(s) the entire continuous-time frequency  from zero to infinity into the discrete-time radian-frequency range zero to π.

(c) Which two methods are almost the same, differing only by a time-domain delay?

(d) Which method can design an unstable digital filter while trying to approximate a stable analog filter and, if constrained to only stable designs, restricts the flexibility of the design to only certain types of filters?