# Using a filter difference equation in a for loop to filter a .wav file within the loop

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Abraham Rodriguez on 8 Dec 2021
Commented: Mathieu NOE on 17 Dec 2021
Based on the bandpass filter difference equation inside a for loop:
x = zeros (30,1);
y = zeros (30,1);
x(3,1) = 1;
for
y(n) = a1*x(n) + a2*x(n-1) + a3*x(n-2) - b1*y(n-1) - b2*y(n-2);
end
How can change a .wav file by running that difference equation through the audio?

Mathieu NOE on 8 Dec 2021
hello
see example below - notice b are usually coeffcient names for numerator so they are used for the x (input) , wheras a coefficients are for the denominator - output y (hence the transfer H = B(z^-1)/A(z^-1))
but you are free to use your own convention as soon as the coeffs have the good value !
enjoy
%% data
[samples,channels] = size(x);
dt = 1/Fs;
time = (0:samples-1)*dt;
%% IIR filter recursive equation
c1 = 8;
c2 = 2;
c3 = 7;
b0 = 0.05 * c1;
b1 = 0.03 * c2;
b2 = 0.02 * c3;
a1 = 0.5;
a2 = 0.5;
% manual for loop coding IIR filter
y(1) = b0*x(1) + 0 + 0 + 0 + 0; % 1st iteration
y(2) = b0*x(2) + b1*x(1) + 0 + a1*y(1) + 0; % 2nd iteration
for k = 3:samples % for iteration # 3 and after
y(k) = b0*x(k) + b1*x(k-1) + b2*x(k-2) + a1*y(k-1) + a2*y(k-2);
end
figure(1)
plot(time,x,time,y)
Mathieu NOE on 17 Dec 2021
hello
problem solved?

R2021a

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