On Feb 18, 2013, at 8:51 PM, robert bristow-johnson wrote: > On 2/18/13 5:55 AM, James C Chandler Jr wrote: >> >> [snip] >> I do not understand the equations that Robert uses to describe filter >> transfer functions. Sometimes in the past I came close to understanding ... > > the document is kinda lazy (actually the author of it is), but i tried to > spell out *how* the analog-to-digital transformation is done at the bottom of > the document. are the analog prototypes a problem, James?
Thanks Robert. There is no problem in the writer, as you have kindly explained at various times the a to d transformation and the s-domain and the z-domain stuff marvelously well in messages over the years, most of which I still have archived. The problem is a reader who has poor memory for some math concepts, and in addition is growing not too sharp in his old age. If I study for a few days I can kinda make sense of s-domain equations but a month later I can't remember and would have to study it all over again, so it is pointless for me to pay much attention to s and z domains unless for some reason it would be 'mission critical' enough to get out the books and refresh once again so I might thrash around trying solve a specific problem. :) Didn't mean to criticize your explanation abilities. The comment was simple disclaimer that the only thing offered was a configuration verified to do multi-band splits that will mix flat. IOW, "this is what you can do, but don't ask me about the equations because I don't know." Was describing essentially what Joshua and others described-- Multiple cascaded 2-way splits. > >> However, was able to use RBJ's cookbook filters to make linkwitz-riley >> filter banks that mix back together "pretty flat". As best I recall, was >> able to get "decently flat" mixing back-together of up to five bands. > > i dunno how to do it for 5 bands other than to repeatedly do the splitting > thing that Joshua Dickenson shown on his site. BTW, Joshua, there has to be > a polarity inversion in there somewhere, either in the HPF transfer function > or in the summer that follows - should subtract instead of add. > > but for 3 bands, i think the 3-band thing on the linkwitzlabs page is better > than splitting into two, and then splitting one of the two again. i think > you can do it with lower order. but for a general N-band crossover, maybe > Joshua's approach is the way to go. and the result should be a perfectly > flat 4th-order all-pass filter. mapping that to the z-domain with bilinear > transform should not change that fact, it should remain perfectly flat. so i > am not sure why you get only "pretty flat" or "decently flat". you should be > getting unqualified "flat". i don't see why not. Thanks for pointing out that http://www.linkwitzlab.com/crossovers.htm link again. Didn't read it carefully enough the first time to realize what he was explaining re the three-band crossover. It is fascinating how he spreads and overlaps the filters to get three "parallel" filters that will mix flat. Six second order filters, compared to nine second order filters in a dual serial two-way split using fourth-order LR filters (plus one second order allpass). I'm not quibbling, but the advantage of throwing more filters at it and doing serial 2-way splits, might be steeper band skirts and more freedom in picking the crossover points, compared to what sounds like a constrained set of crossover frequencies available in that Duelund 3 way parallel crossover? Years ago I wrote a set of L-R multiband splitter code objects for my own use, 2 band up thru 8 band, using series 2-way splits and allpass filters for "fine alignment". If there are not many bands and they are pretty wide, the allpass filters are not so important, but for fairly narrow close-spaced bands the allpass filters seemed necessary to prevent the phases of the different bands diverging and causing a bumpy response when the bands are mixed back together. Took fairly good notes but would need to look them up as my memory sucks. I usually tested the flatness with very slow sine wave sweeps. Greater than about 5 bands did not mix ruler flat. It may have been simple coding error on some of the objects, dunno. Might find time to take a second look some day. Wondered if maybe there was so much phase shift in the "many bands" splitters that a moving-frequency sine wave traveling thru all those phase shifter sections and mixed back together might have caused the "bumpy response" but maybe that is silly talk, dunno. James Chandler Jr. -- 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
