Filter of sin component of sound signal

Hey

This is a project that i am working on, there we are suppose to filter out a sin-component from a small sound signal.

I have the signal "x" already, this "x" contains the sound signal og the energy-spectral-density.

And I have done all the calculations for the filter and signal, and ended up with this differential equation:

y = 2*a*cos(W_s)*y(n-1) - a.^2*y(n-2) - b0*x(n) - b0*2*cos(W_s)*x(n-1) + b0*x(n-2);

So my next step is to get this signal y(n) and check and se if the sin-component is gone. I know that I should be loop like this:

for n =  3:length(x)
    y(n) = 2*a*cos(W_s)*y(n-1) - a.^2*y(n-2) - b0*x(n) - b0*2*cos(W_s)*x(n-1) + b0*x(n-2);
end

But i am getting this error: Attempted to access y(2); index out of bounds because numel(y)=1.

Answer 1

[Youssef Khmou]

Concerning the equation of y, can you explain its origin. As for the error, initial condition must be set :

 y=zeros(size(x));
 y(1)=x(1);
 y(2)=x(2);
 % for loop

[Even Wee]

Sorry, i have the y(n). It is an array of data like x(n), that contains the sound signal with the sin-component that need to be filtered.

So the differential equation is the differential-equation of the filter. And it should be causal, therefore I need to begin on n = 3.

[Even Wee]

Okay.. now i got it to work, and I manage to also filter the sin-component. It was a sign error in my differential-equation, it should be like this

    y = 2*a*cos(W_s)*y(n-1) - a.^2*y(n-2) + b0*x(n) - b0*2*cos(W_s)*x(n-1) + b0*x(n-2);

And i think "y" was not initialized when i got this error: "Attempted to access y(2); index out of bounds because numel(y)=1."

But now it works as it should :)

Thank you.