Re: [music-dsp] 24dB/oct splitter
On 2/8/13 2:15 AM, Ross Bencina wrote: There are a at least two linear SVFs floating round now (the Hal Chamberlin one and Andy Simper's [1] ) [1] http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised.pdf i've analyzed Hal's SVF to death, and i was exposted to Andy's design some time ago, but at first glance, it looks like the Trapazoidal SVF looks like it doubles the order of the filter. it it was a second-order analog, it becomes a 4th-order digital. but his final equations do not show that. do those trapazoidal integrators, become a single-delay element block (if one were to simplify)? even though they ostensibly have two delays? i just did a quick check on the Trapazoidal SVF, and it is identical to using Bilinear Transform without pre-warping and applying BLT directly to the analog filter. so it does not increase the order as it first appeared to me to do. it literally substitutes (assuming T=1): s^-1 ---(1/2)(1 + z^-1)/(1 - z^-1) so they all become 2nd-order biquads and they can be represented in the Direct Form (1 or 2) and compared directly to any other biquad design. for the bell filter, assuming he gets the resonant frequency right (which means dealing with the frequency warping effect), the only possible net difference between *any* design is in how bandwidth or Q turns out. all 2nd-order bell filters are equivalent in their simplified transfer function except in how Q is defined. (well, i guess that's not true for the Orfanidis design. that changes what the gain at Nyquist is and doesn't make any difference if the resonance is more than a couple octaves below Nyquist.) now, what about Andy's Optimised structure with all coefficients remaining bounded [0, 2]? what is the basis for this structure? i can't seem to decode that, and it also appears that the filter has 3 independent delay elements so it's a 3rd-order digital filter emulating a 2nd-order analog filter. i just would like to know where he came up with the structure of this. we know that a digital filter can (if one allows for a little delay) approach the behavior of an analog filter to as close fit as one desires (as long as one is willing to increase the order of the filter and is willing to accept the resulting delay). but i am curious to what the basic philosophy of this Optimised structure is. while Andy explained it for the Trapazoidal SVF, i can't tell by just looking at the drawing for the Optimized what -- r b-j r...@audioimagination.com Imagination is more important than knowledge. -- 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
Re: [music-dsp] 24dB/oct splitter
Hi Russel, you will most certainly not be happy with that. If you put the LP through a second lowpass you get a 24db lowpass If you put the HP output through a lowpass, you get a 12db bandpass If you put the HP output through a second highpass you get a 24db highpass. The problem is, that the 24db lowpass and the 24db highpass don't add together if they are generated from only two SVFs - you will loose mid-frequency content. Also, what ever you do with svfs, use Andy's version (see Ross' email) - it's worth it :-). Cheers, - Clemens Heppner On Feb 8, 2013, at 8:05 AM, Russell Borogove wrote: I have two digital 12dB/octave state-variable filters, each with lowpass/highpass/bandpass/notch outputs; I'd like to use them as a 24db/octave low/high band splitter. Will I be happy if I use the lowpass of the first filter as input to the second, then take the lowpass and highpass outputs of the second as my bands, or do I need to put the low and high outputs of the first filter into two different second stage filters? -Russell Borogove -- 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
Re: [music-dsp] 24dB/oct splitter
On Feb 7, 2013, at 11:15 PM, Ross Bencina wrote: So to be clear, you're creating a Linkwitz-Riley crossover? http://en.wikipedia.org/wiki/Linkwitz%E2%80%93Riley_filter Ahhh, well, I would be if I knew what I was doing. :) You didn't specify which state-variable filter you're using. There are a at least two linear SVFs floating round now (the Hal Chamberlin one and Andy Simper's [1] ) Yeah, I'm using Simper's. Will I be happy if I use the lowpass of the first filter as input to the second, then take the lowpass and highpass outputs of the second as my bands The lowpass output of the first filter presumably has a zero at nyquist, so I don't think this is going to work out well if you highpass it.. you could try though. Yeah, I obviously wasn't thinking straight last night. Thanks everyone. -Borogove -- 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
Re: [music-dsp] 24dB/oct splitter
Hi Russell, So to be clear, you're creating a Linkwitz-Riley crossover? http://en.wikipedia.org/wiki/Linkwitz%E2%80%93Riley_filter On 8/02/2013 6:05 PM, Russell Borogove wrote: I have two digital 12dB/octave state-variable filters, each with lowpass/highpass/bandpass/notch outputs; I'd like to use them as a 24db/octave low/high band splitter. You didn't specify which state-variable filter you're using. There are a at least two linear SVFs floating round now (the Hal Chamberlin one and Andy Simper's [1] ) Will I be happy if I use the lowpass of the first filter as input to the second, then take the lowpass and highpass outputs of the second as my bands The lowpass output of the first filter presumably has a zero at nyquist, so I don't think this is going to work out well if you highpass it.. you could try though. or do I need to put the low and high outputs of the first filter into two different second stage filters? That's my impression. Ross [1] http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised.pdf -- 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
Re: [music-dsp] 24dB/oct splitter
On Fri, Feb 8, 2013 at 8:05 AM, Russell Borogove kal...@estarcion.com wrote: Will I be happy if I use the lowpass of the first filter as input to the second, then take the lowpass and highpass outputs of the second as my bands, or do I need to put the low and high outputs of the first filter into two different second stage filters? If I'm thinking straight, the LP output of the first filter won't contain more than the difference between a 12 and 24 dB/oct filter - so the HP output of the second filter would be almost silent. I think you need separate filters for the second stage. -- //David Olofson - Consultant, Developer, Artist, Open Source Advocate .--- Games, examples, libraries, scripting, sound, music, graphics ---. | http://consulting.olofson.net http://olofsonarcade.com | '-' -- 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
