layering opposing eq to acheive phase shift

So just thinking out loud really ....


Just wondering about the phase summation of two opposite filters !

For example ....

1) -3db @100 Hz q= 2.6
2) +3db @100 Hz q= 2.6

Frequency curve will be as if no eq had been applied but what about phase responce , will it be 0 or will it be 45 degrees difference ??

Does the answer to the question change if it's a passive design or a digital design ?

Just thinking about ways to manipulate group delay


Edited by matty w - 24 May 2017 at 11:15am

matty w wrote: So just thinking out loud really .... Just wondering about the phase summation of two opposite filters ! For example .... 1) -3db @100 Hz q= 2.6 2) +3db @100 Hz q= 2.6 Frequency curve will be as if no eq had been applied but what about phase responce , will it be 0 or will it be 45 degrees difference ?? Does the answer to the question change if it's a passive design or a digital design ? Just thinking about ways to manipulate group delay

Ignoring the type of filter and getting down to root transfer functions a bandpass filter with positive gain is going to be a group of poles situated near the centre frequency +-Wo on the left hand side of the complex plan y-axis.

Exactly the same filter in terms of (Wo, Q) but with negative amplitude will have zeros on the same locations. Phase shift is the sum of the angles from a point on the y-axis representing a frequency jw to all of the poles and zeros. Because they are in the same locations exactly then for any frequency it is pretty easy to show that there will always be zero phase shift due to the convolution of the filters. If you multiplied their transfer functions together then the result would almost certainly be unity, but I can't be arsed to try it :)

If you were clever there is probably a way of cascading filters in such a way to manipulate phase shift, but as was already said you'd probably be better off trying to do it with poles and zeros outside of your audio bandwidth of interest.