# Thread: Fastest roll-off of a filter

1. ## Fastest roll-off of a filter

I was wondering: can a filter be optimised to have maximum roll off. Filters are usually specified as:
$|H(\omega)|^2 = \frac{1}{1 + \alpha(\omega)}$ where $\alpha$ is a polynomial function. I was wondering if it was possible to maximise the steepness of the roll-off by specifying the passband and stopband ripples.

What is usually done is:
$|H(\omega)|^2 = H(\omega)H(-\omega) = \frac{1}{1 + \alpha(\omega)}$
This gives you the polls and zeros. Then you'll need to do some optimisation of some kind.

2. ## Re: Fastest roll-off of a filter

Optimum "L" filter - Wikipedia, the free encyclopedia particular the two references in the bibliography.

Maximum roll off usually means undesired characteristics somewhere else, such as too much passband ripple or phase distortion.