Filter slopes

Harry Bissell harrybissell at prodigy.net
Tue Nov 2 08:23:31 CET 1999


EEK... heres my $2/100

1) Filters can be any number of db, but thet are easy in multiples of 6 db.
There is a way to cascade filter sections to get partial ccancellation of
poles and zeros and get inbetween responses. Probably not too easy if you are
talking VCF here...
Check our "math majors" on the list...

2) If you tap the same filter at two points (usually the 12 and 24 db, but i
guess 6 and 12 might work also) and take the difference you get a bandpass.
Don't know if you sum them... I'll try a simulation sometime.

:^) Harry

Tom May wrote:

> Brian.Dekok at ca.jdsunph.com writes:
>
> > Can filters slopes be obtained in other multiples than 6dB/oct? For
> > example, I feed a signal to a first-order and a second-order filter
> > in parallel, with the same fc. If the outputs are mixed together,
> > what is the final slope of the filtered signal?
>
> You'll probably get thousands of answers, but here goes.  Intuitively,
> it will be only 6dB/oct because at high frequencies, the 12dB/oct
> filter is letting negligible signal through and the 6dB/oct is only
> filtering at 6dB/oct.
>
> Here's the frequency domain math:
>
>                               1
> 6dB/oct filter response is  -----
>                             (s+1)
>
>                                1
> 12dB/oct filter response is -------
>                             (s+1)^2
>
>              s+2
> The sum is -------  which for large s becomes 1/s which is a 6dB rolloff.
>            (s+1)^2
>
> It intially rolls of a bit more steeply than a 6dB/oct filter because
> of the double pole at s = -1, but the zero at s = -2 counteracts that.
>
> fTom.




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