Implementing Notch filter for an audio signal

Hello, I have the folowing filter expressed as an equasion

If you put in Exel for example values from 0khz to 15khz in 1Hz increments, you get a response that looks like this

WolfranAlpha draws it like this: https://www.wolframalpha.com/input?i=%281+%2B+i*6.4*f%29+%2F+%285+%2B+i*6.4*f%29

Now when I wanted to implement this in matlab, and used this audio sample: https://transfer.sh/ruffRk/test.wav

[y,Fs] = audioread('test.wav'); 

filtered = (1+1i*6.4*y)/(5+1i*6.4*y);

sound(filtered,Fs);

I got the folowing error

Error using  / 
Requested 3888467x3888467 (225308.2GB) array exceeds maximum array size
preference (32.0GB). This might cause MATLAB to become unresponsive.

Now I don't know how to implement this notch filter properly in matlab, I guess its just requires too much RAM, that I don't have or is there any other way?

Thanks for Anwsering and Best Regards

[Scott MacKenzie]

What frequency are you trying to filter out? Have you tried using one of MATLAB's filter functions, such as bandstop?

[Mitja Kocjancic]

That's the problem, I don't realy know, the documentation only says that I need to filter out according to this formula

and here is a picture to make it clearer what I am trying to do

the top signal is how this signal is supposed to look like (and the formula describes the procedure to do so), the bottom is the original signal (not filtered by this formula)

[Scott MacKenzie]

I'm not sure how to set this up, based on the formula and images you've posted. There are some STAFF and MVP contributors that are quite knowledgeable on this. Hopefully, one of them will weigh in with some suggestions. Good luck.

[Mathieu NOE]

hello

maybe I'm wrong, but seems to me that the modulated signal must simply goes through a one pole one zero filter

(for me j*f = p /(2*pi) , p being the Laplace variable)

so this filter can be rewritten as K(p) = (1+6.4/(2*pi)*p ) / (5 + 6.4/(2*pi) *p)

num = [6.4/(2*pi)   1];
den =  [6.4/(2*pi)   5];

you can then discretize this filter using bilinear or c2dm to filter your audio file

[Mitja Kocjancic]

@Mathieu NOE you made my day, thanks man, not sure how to accept this anwser but yey it finaly works :)

now I have it like this

function result = k_notch(signal, phase, Fs)

disp("Applying Notch filter for: " + phase);

num = [6.4/(2*pi) 1];

den = [6.4/(2*pi) 5];

%Discrete this

[ad, bd] = bilinear(num, den, Fs);

%Filter signal

result = filter(ad,bd,signal);

end

and I am happy :)

[Mathieu NOE]

My pleasure !