# Sound equalization : assumptions around the use of the transfer functions. Are they correct?

I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check.

1/ I'm applying the continuous transfer function (low-cut, high-cut or passband filters) to a sampled signal. As my sampled signal have a plot each 20 Hz for example (= my spectral precision), I don't care about the value of the transfer fonction for the band 315 Hz : I will only use the value at 300 Hz or 320 Hz given by the transfer function. Is it correct ?

2/ I want to modify the gain of the signal around a frequency (central frequency +- quality factor) so, I'm using the modulus of the transfer function. My signal frequency is a complex and multiplying a complex by a real coefficient (the modulus) will change the amplitude but not the phasis (argument). Is it correct ?

3/ It was the trickyest point. Which value do I have to apply to the "K" (gain) factor of the tranfer function to sculpt my signal ? I my mind, if gain=1, I should get the signal without any transform. But if K=1 in the transfer function, I will get an attenuation outside of the passban and a "native" signal inside the passband. So, I decided to add "1" to my calculated gain and to allow negative values to the gain.

So, for example, if K=0 => gain = 1 everywhere ; if K=1 => gain = 1 outside the passband and goes until +2 (+3db) inside the passband ; if K=-0.5 => gain = 1 outside the passband and decrease until -0.5 (-3db) inside the passband. Does this calculation assumption seems correct ?

Note : the modulus of the transfer function I'm using for the passband filter is :

|H| = K / (1 + Q^2.(x - 1/x)^2 )^0.5 with K = gain, Q = quality factor, x = signal frequency / central frequency