Well, you're already working with rbj's equations, so just multiple the numerator coefficients by A^2...
On Jan 3, 2013, at 1:05 PM, Nigel Redmon <earle...@earlevel.com> wrote: > OK, I had (well, took) time to think: > > You need to divide the numerator by the gain (A), and multiple the > denominator by the gain (aka multiply the numerator by A^2). That will keep > the peak at unity. Swap the numerator and denominator if you want the EQ to > be symmetric for cut and boost. If you need the BLT worked out, let me know. > > > On Jan 3, 2013, at 11:03 AM, Thomas Young <thomas.yo...@rebellion.co.uk> > wrote: > >> Thanks Nigel - I have just been playing around with the pole/zero plotter >> (very helpful app for visualising the problem) and thinking about it. You >> guys are probably right the simplest approach is just to scale the output >> and using the peaking filter. >> >> Additional optional mumblings: >> >> I think really there are two 'correct' solutions to manipulating only the >> coefficients to my ends (that is, generation of coefficients which produce >> filters interpolating from bandpass to flat): >> >> The first is to go from pole/zero to transfer function, basically as you >> (Nigel) described in your first message - stick the zeros in the centre, >> poles near the edge of the unit circle and reduce their radii - doing the >> maths to convert these into the appropriate biquad coefficients. This isn't >> really feasible for me to do in realtime though. I was trying to do a sort >> of tricksy workaround by lerping from one set of coefficients to another but >> on reflection I don't think there is any mathematical correctness there. >> >> The second is to have an analogue prototype which somehow includes skirt >> gain and take the bilinear transform to get the equations for the >> coefficients. I'm not really very good with the s domain either so I >> actually wouldn't know how to go about this, but it's what I was originally >> thinking of. >> >> Thanks for the help >> >> -----Original Message----- >> From: music-dsp-boun...@music.columbia.edu >> [mailto:music-dsp-boun...@music.columbia.edu] On Behalf Of Nigel Redmon >> Sent: 03 January 2013 18:48 >> To: A discussion list for music-related DSP >> Subject: Re: [music-dsp] Lerping Biquad coefficients to a flat response >> >> Thomas-it's a matter of manipulating the A and Q relationships in the >> numerator and denominator of the peaking EQ analog prototypes. I'm not as >> good in thinking in the s domain as the z, so I'd have to plot it out and >> think-too busy right now, though it's pretty trivial. But just doing the >> gain adjustment to the existing peaking EQ, as Ross suggested, is trivial. >> Not much reason to go through the fuss unless you're concerned about adding >> a single multiply. (To add to the confusion, my peaking implementation is >> different for gain and boost, so that the EQ remains symmetrical, a la >> Zolzer). >> >> >> On Jan 3, 2013, at 9:34 AM, Thomas Young <thomas.yo...@rebellion.co.uk> >> wrote: >> >>>> I'm pretty sure that the BLT bandpass ends up with zeros at DC and >>>> nyquist >>> >>> Yes I think this is essentially my problem, there are no stop bands per-se >>> just zeros which I was basically trying to lerp away - which I guess isn't >>> really the correct approach. >>> >>> The solution you are proposing would work I believe; along the same lines >>> there is a different bandpass filter in the RBJCB which has a constant stop >>> band gain (or 'skirt gain' as he calls it) and peak gain for the passband - >>> so a similar technique would work there by scaling the output. >>> >>> However I was hoping to avoid scaling the output since if I have to do that >>> then I might as well just change the wet/dry mix with the original signal >>> for essentially the same effect and less messing about. I feel in my gut >>> there must be some way to do it by just manipulating coefficients. >>> >>> >>> -----Original Message----- >>> From: music-dsp-boun...@music.columbia.edu >>> [mailto:music-dsp-boun...@music.columbia.edu] On Behalf Of Ross >>> Bencina >>> Sent: 03 January 2013 17:16 >>> To: A discussion list for music-related DSP >>> Subject: Re: [music-dsp] Lerping Biquad coefficients to a flat >>> response >>> >>> On 4/01/2013 4:05 AM, Thomas Young wrote: >>>> Is there a way to modify the bandpass coefficient equations in the >>>> cookbook (the one from the analogue prototype H(s) = s / (s^2 + s/Q + >>>> 1)) such that the gain of the stopband may be specified? I want to be >>>> able >>> >>> I'm pretty sure that the BLT bandpass ends up with zeros at DC and >>> nyquist so I'm not sure how you're going to define stopband gain in >>> this case :) >>> >>> Maybe start with the peaking filter and scale the output according to your >>> desired stopband gain and then set the peak gain to give 0dB at the peak. >>> >>> peakGain_dB = -stopbandGain_dB >>> >>> (assuming -ve stopbandGain_dB). >>> >>> Does that help? >>> >>> Ross. >>> -- >>> dupswapdrop -- the music-dsp mailing list and website: >>> subscription info, FAQ, source code archive, list archive, book >>> reviews, dsp links http://music.columbia.edu/cmc/music-dsp >>> http://music.columbia.edu/mailman/listinfo/music-dsp >>> -- >>> dupswapdrop -- the music-dsp mailing list and website: >>> subscription info, FAQ, source code archive, list archive, book >>> reviews, dsp links http://music.columbia.edu/cmc/music-dsp >>> http://music.columbia.edu/mailman/listinfo/music-dsp >> >> -- >> dupswapdrop -- the music-dsp mailing list and website: >> subscription info, FAQ, source code archive, list archive, book reviews, dsp >> links http://music.columbia.edu/cmc/music-dsp >> http://music.columbia.edu/mailman/listinfo/music-dsp >> -- >> dupswapdrop -- the music-dsp mailing list and website: >> subscription info, FAQ, source code archive, list archive, book reviews, dsp >> links >> http://music.columbia.edu/cmc/music-dsp >> http://music.columbia.edu/mailman/listinfo/music-dsp > > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, dsp > links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
