How do I design filters using Z transfer functions?

I have a paper on ECG segmentation, and need to develop an algorithm using Matlab that involves among other things, developing 2 filters (a Low Pass Differentiator and a First-Order Low Pass Filter) that have the following transfer functions:

Gdiff(z)=1-z^(-6)

and

Gsmooth(z)=(1-z^(-8))/(1-z^(-1))

Any suggestions are welcome. Thank you.

[Jonathan Epperl]

z = tf('z', Ts); % Ts is your sampling time
Gdiff = 1-1/z^6;

In any case, do

doc tf

that will provide you with all you need to know about transfer functions in Matlab.

[Dragos Alexandru MOCANU]

Thank you very much for the insight, but is there any way to convert the transfer function into a filter?

Answer 1

[Honglei Chen]

It is straightforward to convert transfer function to filter (in theory) to filter coefficients, as shown in the following wiki

http://en.wikipedia.org/wiki/Digital_filter

For example, you Gdiff is an FIR filter with coefficients of [1 0 0 0 0 0 -1]