Read about inpulse response invariance filter design method.

See my lecture on the subject attached.

Summarising the impulse invariance method:

1. start off with the analogue filter transfer function H(s);

2. apply partial fractions to factorise H(s);

3. split into linear and quadratic factors that will give you real and complex exponentials;

4. apply inverse Laplace transform to find components of h(t), i.e., obtain the impulse response of the continuous system;

5. sample h(t) to obtain hn for the discrete system (be careful with the choice of the sampling period here!);

6. find z-transform for each of the factors;

7. assemble the z-transfer function;

8. from H(z) write down the difference equation;

9. implement it.