# No Subject

Fluke Cloudrunner fcloudrunner at hotmail.com
Sat Oct 17 02:56:01 EDT 1998

```Hi all,

In his post about biquad filter coef calculations, R. B-J shows the
formulae below, which I understand for the most part. Now if I want a
LPF or HPF, the coefs need the 'alpha', which has a Q in its definition.

Sorry if I missed this issue earlier, but this post is the reason I
joined the list.

So what does the Q control in the case of LPF and HPF?

Plus I recently purchased a book by Udo Zoelzer (Digital Audio Signal
Processing) that shows similar formulae for these kind of filters. I
plan to compare and determine the differences of definitions and
behavior. Anybody did it already and have any comment?

Thanks

fc

>A = sqrt[ 10^(dBgain/20) ] = 10^(dBgain/40)
>omega = 2*PI*frequency/sample_rate
>cs = cos(omega)
>sn = sin(omega)
>Q = sn/[ ln(2)*bandwidth*omega ]    (if bandwidth is specified >instead
of Q)
>
>alpha = sn*sinh[ 1/(2*Q) ]
>beta = sqrt[ (A^2 + 1)/S - (A-1)^2 ]
>
>
>then compute the coefs for whichever filter type you want:
>
>LPF:            b0 = (1 - cs)/2
>                b1 =  1 - cs
>                b2 = (1 - cs)/2
>                a0 =  1 + alpha
>                a1 = -2*cs
>                a2 =  1 - alpha.
>
>HPF:            b0 = (1 + cs)/2
>                b1 = -1 - cs
>                b2 = (1 + cs)/2
>                a0 =  1 + alpha
>                a1 = -2*cs
>                a2 =  1 - alpha

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