On Mon, 11 Feb 2013 12:52:00 -0500 robert bristow-johnson <r...@audioimagination.com> wrote:
> On 2/11/13 11:43 AM, Johannes Kroll wrote: > > On Mon, 11 Feb 2013 10:28:17 -0500 > > robert bristow-johnson<r...@audioimagination.com> wrote: > > > >> On 2/10/13 12:13 PM, Johannes Kroll wrote: > >>> On Sun, 10 Feb 2013 03:23:54 -0800 > >>> Bram de Jong<bram.dej...@gmail.com> wrote: > >>>> does anyone know of a filter design that can smoothly be changed from > >>>> LP to BP to HP with a parameter? IIRC LP/AP/HP could be done simply by > >>>> perfect reconstruction LP/HP filter pairs, but never seen something > >>>> similar for BP in the middle... > >>>> > >>>> The filter doesn't need to be "perfect", it's for something > >>>> musical/creative rather than a purely scientific goal... > >>> This may sound naive, but would it not be possible to chain an LP and a > >>> HP filter in series and adjust their dry/wet rates according to > >>> parameter? > >>> > >> it's not naive (but it's parallel, not chained in series) and at one > >> time in the distant past, we called that the "Tone" control. > > I was serious :) It's not a single filter design, but it should do, > > right? > > > > And to get a BP you would have to chain LP+BP in series, not in > > parallel, no? ... Perhaps I misunderstood what Bram wants to do. > > > > well, if they're in series, changing the gain on any component in the > chain merely changes the gain on the whole thing. it does not change > the shape. so i am not completely understanding what you're suggesting. Not the gain, the dry/wet ratio, i.e. the amount of signal which gets passed through the filter untouched vs the filtered signal. If you pass the signal through an LP first, and the result through a HP, you get a BP. If you then adjust the dry/wet ratio of both filters, you should get something that smoothly fades between LP, BP and HP. So you would use an input parameter P (0..1), and the wet ratio of the LP and HP. At P=0.0, set LPwet to 1.0 and HPwet to 0.0 (pure lowpass) At P=0.5, set LPwet to 1.0 and HPwet to 1.0 (bandpass) At P=0.0, set LPwet to 0.0 and HPwet to 1.0 (pure highpass) Where XPwet is the dry/wet ratio, 0 is completely filtered and 1 is completely unfiltered (the original signal). Put these three points in a table and do linear interpolation between them for values of P. So with P=0.25, you get LPwet=1.0 and HPwet 0.5, which is a 50/50 mix between LP and BP... And so on. You would probably choose slightly different frequencies for the LP and HP, depending on how steep the filters are and how large you want the BP to be. May not be the most elegant way but it should be easy to do if you already have the LP and HP filters as building blocks. It could even be done in something like puredata, without writing code. I thought that was kind of what the OP wanted. > i don't know how to get BP in the middle of an LP and HP without > introducing a sorta quadratic gain function. > > suppose you have three filters, LPF, BPF, and HPF (let's say you get > them outa the cookbook) all with the same resonant frequency and Q. now > let's say you have a control parameter, u, that is -1 for LPF, 0 for > BPF, and +1 for HPF. you can come up with a set of 2nd-order Lagrange > polynomials ( http://en.wikipedia.org/wiki/Lagrange_polynomial ) that > will go through 1 for the filter you want and takes on 0 for the two > filters you don't want. > > for LPF it is: gain_LP(u) = (1/2)*u*(u-1) > > for BPF it is: gain_BP(u) = (-1)*(u+1)*(u-1) > > for HPF it is: gain_HP(u) = (1/2)*u*(u+1) > > attach those gains to the corresponding filters and add the results > (filters in parallel) of those weighted filters. if you're using the > cookbook (or most other definitions), you will see that the denominator > coefficients are the same for all three filters, so these gain factors > apply only to the numerator coefs. you can smoothly pass from purely > LPF, through purely BPF, up to a purely HPF as u moves from -1 through 0 > up to +1. So you would in effect subtract parts of the filter outputs from the signal? Would that not give problems when the filters create phase variances at different frequencies? (Disclaimer: I don't completely understand the maths behind what you posted and I'm not a filter expert :) -- 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
