How do filter function work?

I understand how the filter(b,a,X) works. What confuses me is the function with the initial conditions. The function filter(b,a,X,zi).

for example: y(n)=-0.5y(n-1)+x(n) x(n)=u(n) y(-1)=1

how will the filter function solve this? i tried to do it manually, but i get different output.

Answer 1

[Honglei Chen]

MATLAB's filter() function an implementation of direction form II, the detailed algorithm can be found at

http://www.mathworks.com/help/techdoc/ref/filter.html#f83-1015962

For your case, you need to first figure out what the initial condition is. You can use filtic function.

http://www.mathworks.com/help/toolbox/signal/ref/filtic.html

e.g.,

b = 1;
a = [1 0.5];
y = filter(b,a,ones(10,1),filtic(b,a,1));

[Treant]

thank you very much! that helps a lot. one last question. how can i solve the output of the filtic function manually.

[Honglei Chen]

It basically perform a reverse filtering operation. If you want the details, you can look at filtic code.

[Sergio Cuadros]

Hello Mr. Honglei, Could you check my question. I have a issue.

https://uk.mathworks.com/matlabcentral/answers/549705-why-filtic-function-does-not-work-for-a-specific-use?s_tid=prof_contriblnk

Best regards.

Answer 2

[Jan]

You find a Matlab implementation of the FILTER command at Answers: hard-code-filter. This should reveal the meaning of the initial and final conditions.

Splitting a signal into parts might be helpful also:

signal = rand(1,1000);
[b,a] = butter(3, 0.5);  % Arbitrary filter parameters

inital_cond1 = zeros(1, length(a) - 1);
[filtered1, final_cond1] = filter(b, a, signal(1:500), initial_cond1);
[filtered2, final_cond2] = filter(b, a, signal(501:1000), final_cond1);
Joined = [filtered1, filtered2];

% Now filter in one step:
OnePiece = filter(b, a, signal, initial_cond1);

% Compare the results - should be tiny:
disp(mean(abs(Joined - OnePiece)));

This shows, that the inital conditions are the values of the internal status of the filter. When the signal is split into pieces, the final conditions of the former part are the inital conditions of the current part.