how to design a high-pass IIR filter having the transfer funciton ?

Hi everyone,

i need to filter a signal with a high-pass IIR filter characterized by a transfer function as follow:

H(z) = 1-z^-1 / 1- a * z^-1

i know a = 0.995 and cut off frequency f = 0.25 Hz

i need to filter the sequence one time in forward direction and then in reversed.

Someone can help me ?

Thank you a lot :)

Answer 1

[Mathieu NOE]

Here you are my friend

I don't know what sequence was supposed to be filtered , so the demo is on random signal

% IIr filter
fc = 0.25; 
a = 0.995;
numd = [1 -1];
dend = [1 -a];

Fs = fc/(1-a)*2*pi;

% signal (random)
dt = 1/Fs;
samples = 3000;
t = (0:samples-1)'*dt;
x = randn(samples,1);

figure(1)
dbode(numd,dend,dt); % bode plot

y = filtfilt(numd,dend,x);  % Zero-phase forward and reverse digital IIR filtering.
% y = filter(numd,dend,x);  % forward digital IIR filtering.

figure(2) % time plot
plot(t,x,t,y);
legend('input signal','output signal');

[Giorgia Fusaroli]

THANK YOU SO MUCH !

[Mathieu NOE]

My pleasure !

[Giorgia Fusaroli]

I have a question for you .. how the filter know the cut off frequency ?

i have a signal acquired with a frequency of 142 Hz

[Mathieu NOE]

Ok so that was the unknown I was looking for

indeed fc, a and Fs are linked together (Fs = fc/(1-a)*2*pi;)

I checked this again with the Bode plot

as you specified a and fc I could find Fs ;

but if you still want fc = 0.25 Hz with Fs = 142 Hz, then a must be modified

[Giorgia Fusaroli]

Okok, i understood and thank you so much for the helping !

I'm trying to replicate a filter so fc = 0.25 and a = 0.995 and the transfer function were given to me.

The original filter is applied to a signal acquired at 200 Hz, this is why it doesn't work for me ?

And to work in my case, what and how should do i change the parameters of the filter ?

[Mathieu NOE]

well , now if fc and Fs are given , you can easily compute the a value :

a = 1 - 2*pi*fc/Fs;

Answer 2

[Giorgia Fusaroli]

I have to day, the filter seems to only tranlsate the signal without modify it :(

[Mathieu NOE]

no surprise

this is a low frequency high pass filter

it will only remove the mean (DC) value of the signal , which appears on your graph as a vertical shift; the "dynamic" portion of the signal remains unchanged as the filter has no effect above 0.25 Hz