Scoofy
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Butterworth flat summing in Audio crossover...
editHello,
I saw that you have mentioned in the article that crossing over the Butterworth filters at -6dB gives flat summing...how is that? I haven't tried it but would be interested to know. Also if they can sum flat then why is it not used in audio? There has to be a compelling reason for it, after all a maximally flat amplitude response is desirable, isn't it? I will do some investigation of my own in the meanwhile...however as a note to both of us, personal research is deemed inappropriate for inclusion in wikipedia articles. Rohitbd 08:28, 10 May 2006 (UTC)
- I was trying to experiment with making a crossover using Butterwort filters, and I realized that if I put the filters further away from each other, the sum will become nearly flat. Here the lowpass filter's -3dB frequency is 1000 Hz, the highpass filters's -3dB freq is 1700 Hz, so this makes a crossover with a crossover freq of 1350 Hz. You can see on the graph that the filter have a -6dB gain at that point. The sum of them gives a nearly flat line, with less than 1dB ripple. If we consider Bessel filter's summed output nearly flat, then this should be considered flat, too. However, this is just an estimation, correct normalisation values could be calculated by solving the Butterworth filter's magnitude equation for -6dB. However, this is probably not used because there isn't big difference between this and the LR2 filter, both have 12dB/oct slopes, the LR2 having a bit softer knee, but the LR2 has the advantage of a completely flat response, with no coloration. Also LR2 has a constant group delay, and linear phase response, whereas the Butterworth does not, which is generally unwanted. All this makes us prefer the LR2. (comparison) Remember, in the world of crossovers it is not maximally flat amplitude that is preferred regarding the individual filters, but the flat summed output, linear phase response and constant group delay. I don't know if this has ever been published anywhere, or anyone uses this technique. The sentence we cannot cross Butterworth filters over at -6dB was not true, so I could either #1 remove the sentence completely #2 add a correction remark. I did the latter one. If you feel that this counts as personal research, or not appropriate for mentioning in the article, feel free to remove it.scoofy 09:09, 10 May 2006 (UTC)
- Personal research is when you write something based on something done by you - of course I have no problem with it but wikipedia norms require that articles are based purely on published material - that too belonging to someone other than the one who's writing the article (I also have been "reprimanded" - so to speak - a couple of times). Regarding why butterworth is not used, I have made the change in the article - and non-linear phase variable group delay, etc. seems to be the only plausible reason for not using butterworth if what you say about flat summing of butterworth is taken into account. Rohitbd 15:21, 11 May 2006 (UTC)
- I think it is a pretty straightforward method to construct Butterworth crossovers like that, similar techinque (normalization) is often used for Bessel filters. I think it is possibly that someone has already published this somewhere, for example, there's a mention in this article from 1980 (do a text search for 6 dB of attenuation in the article). I suppose when Linkwitz-Riley and Bessel crossovers became more common, they did not use that anymore, because the latter ones are simply better (better phase response or flatter summing). I think the Audio crossover aritle is much better now that it is shortened and lots of text was removed that is not relevant from a practical point of view.
- Personal research is when you write something based on something done by you - of course I have no problem with it but wikipedia norms require that articles are based purely on published material - that too belonging to someone other than the one who's writing the article (I also have been "reprimanded" - so to speak - a couple of times). Regarding why butterworth is not used, I have made the change in the article - and non-linear phase variable group delay, etc. seems to be the only plausible reason for not using butterworth if what you say about flat summing of butterworth is taken into account. Rohitbd 15:21, 11 May 2006 (UTC)
- I was trying to experiment with making a crossover using Butterwort filters, and I realized that if I put the filters further away from each other, the sum will become nearly flat. Here the lowpass filter's -3dB frequency is 1000 Hz, the highpass filters's -3dB freq is 1700 Hz, so this makes a crossover with a crossover freq of 1350 Hz. You can see on the graph that the filter have a -6dB gain at that point. The sum of them gives a nearly flat line, with less than 1dB ripple. If we consider Bessel filter's summed output nearly flat, then this should be considered flat, too. However, this is just an estimation, correct normalisation values could be calculated by solving the Butterworth filter's magnitude equation for -6dB. However, this is probably not used because there isn't big difference between this and the LR2 filter, both have 12dB/oct slopes, the LR2 having a bit softer knee, but the LR2 has the advantage of a completely flat response, with no coloration. Also LR2 has a constant group delay, and linear phase response, whereas the Butterworth does not, which is generally unwanted. All this makes us prefer the LR2. (comparison) Remember, in the world of crossovers it is not maximally flat amplitude that is preferred regarding the individual filters, but the flat summed output, linear phase response and constant group delay. I don't know if this has ever been published anywhere, or anyone uses this technique. The sentence we cannot cross Butterworth filters over at -6dB was not true, so I could either #1 remove the sentence completely #2 add a correction remark. I did the latter one. If you feel that this counts as personal research, or not appropriate for mentioning in the article, feel free to remove it.scoofy 09:09, 10 May 2006 (UTC)
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