On Aug 1, 9:56�am, Andor <andor.bari...@gmail.com> wrote:> On 1 Aug., 06:11, robert bristow-johnson <r...@audioimagination.com> > wrote: > > > you can, but the sum-of-cosine (which are more generally sum-of- > > exponentials), whether they be TIIR or simply FIR, do not have simply > > a rational transfer function, do they? > > Of course they do. Maybe I should post an example? >okay, i accept that they have rational transfer functions, but they're of very high order because of the delay line. but Andor, i am still curious about the "not LTI" idea. i think, that if the word width was arbitrarily wide, it would be LTI to within any measure. for a given word width, there would be a reasonable error metric, that you could make smaller and smaller, with this Powell/Chau combined with TIIR will be a real-time system that is LTI. the time-variant stuff inside largely cancels itself out. r b-j
removing phase shift - reversing the signal
Started by ●July 26, 2009
Reply by ●August 1, 20092009-08-01
Reply by ●August 3, 20092009-08-03
On 2 Aug., 00:08, robert bristow-johnson <r...@audioimagination.com> wrote:> On Aug 1, 9:56�am, Andor <andor.bari...@gmail.com> wrote: > > > On 1 Aug., 06:11, robert bristow-johnson <r...@audioimagination.com> > > wrote: > > > > you can, but the sum-of-cosine (which are more generally sum-of- > > > exponentials), whether they be TIIR or simply FIR, do not have simply > > > a rational transfer function, do they? > > > Of course they do. Maybe I should post an example? > > okay, i accept that they have rational transfer functions, but they're > of very high order because of the delay line. �but Andor, i am still > curious about the "not LTI" idea. �i think, that if the word width was > arbitrarily wide, it would be LTI to within any measure. �for a given > word width, there would be a reasonable error metric, that you could > make smaller and smaller, with this Powell/Chau combined with TIIR > will be a real-time system that is LTI. �the time-variant stuff inside > largely cancels itself out.Perhaps there was a misunderstanding on my part. To sum it up: Powell/Chau -> linear periodically time-variant system Powell/Chau with TIIR modification -> LTI system (up to roundoff). On the other topic: should I post an example of a sum-of-cosines windowed TIIR filter? Regards, Andor
Reply by ●August 4, 20092009-08-04
On Aug 3, 4:04�am, Andor <andor.bari...@gmail.com> wrote:> On 2 Aug., 00:08, robert bristow-johnson <r...@audioimagination.com> > wrote: > > > > > On Aug 1, 9:56�am, Andor <andor.bari...@gmail.com> wrote: > > > > On 1 Aug., 06:11, robert bristow-johnson <r...@audioimagination.com> > > > wrote: > > > > > you can, but the sum-of-cosine (which are more generally sum-of- > > > > exponentials), whether they be TIIR or simply FIR, do not have simply > > > > a rational transfer function, do they? > > > > Of course they do. Maybe I should post an example? > > > okay, i accept that they have rational transfer functions, but they're > > of very high order because of the delay line. �but Andor, i am still > > curious about the "not LTI" idea. �i think, that if the word width was > > arbitrarily wide, it would be LTI to within any measure. �for a given > > word width, there would be a reasonable error metric, that you could > > make smaller and smaller, with this Powell/Chau combined with TIIR > > will be a real-time system that is LTI. �the time-variant stuff inside > > largely cancels itself out. > > Perhaps there was a misunderstanding on my part. To sum it up: > > Powell/Chau -> linear periodically time-variant system > Powell/Chau with TIIR modification -> LTI system (up to roundoff).it seems to me that the intent of Powell/Chau (they weren't considering TIIR) was to let the tail die to such a low level that they could hack it off with the time-variant error signal being arbitrarily small. they would have to wait much longer than if a TIIR was used, i think. it was meant to be, within roundoff or some other error constraint, LTI.> On the other topic: should I post an example of a sum-of-cosines > windowed TIIR filter?sure, whinot? r b-j
Reply by ●August 4, 20092009-08-04
On 4 Aug., 06:24, robert bristow-johnson <r...@audioimagination.com> wrote:> On Aug 3, 4:04�am, Andor <andor.bari...@gmail.com> wrote: > > > > > > > On 2 Aug., 00:08, robert bristow-johnson <r...@audioimagination.com> > > wrote: > > > > On Aug 1, 9:56�am, Andor <andor.bari...@gmail.com> wrote: > > > > > On 1 Aug., 06:11, robert bristow-johnson <r...@audioimagination.com> > > > > wrote: > > > > > > you can, but the sum-of-cosine (which are more generally sum-of- > > > > > exponentials), whether they be TIIR or simply FIR, do not have simply > > > > > a rational transfer function, do they? > > > > > Of course they do. Maybe I should post an example? > > > > okay, i accept that they have rational transfer functions, but they're > > > of very high order because of the delay line. �but Andor, i am still > > > curious about the "not LTI" idea. �i think, that if the word width was > > > arbitrarily wide, it would be LTI to within any measure. �for a given > > > word width, there would be a reasonable error metric, that you could > > > make smaller and smaller, with this Powell/Chau combined with TIIR > > > will be a real-time system that is LTI. �the time-variant stuff inside > > > largely cancels itself out. > > > Perhaps there was a misunderstanding on my part. To sum it up: > > > Powell/Chau -> linear periodically time-variant system > > Powell/Chau with TIIR modification -> LTI system (up to roundoff). > > it seems to me that the intent of Powell/Chau (they weren't > considering TIIR) was to let the tail die to such a low level that > they could hack it off with the time-variant error signal being > arbitrarily small. �they would have to wait much longer than if a TIIR > was used, i think. �it was meant to be, within roundoff or some other > error constraint, LTI.Look at Fig. 11 in their paper. They were well aware of the harmonic distortion due to modulation of the length of the impulse response.> > > On the other topic: should I post an example of a sum-of-cosines > > windowed TIIR filter? > > sure, whinot?As of tomorrow I am on vacation for a week. Maybe I can squeeze some time out in between, but no promises. Regards, Andor
