Hi, It is known that time-varying may make an IIR unstable even it is stable on its own. Imposing limits on the amount of varying is able to eliminate this possibility of becoming unstable. I am wondering, is there a cookbook formula I can obtain these limits on fc, Q or gain? Thanks a lot. SYL
stability of time-varying biquad
Started by ●October 28, 2008
Reply by ●October 28, 20082008-10-28
On Oct 28, 2:00�pm, SYL <sya...@gmail.com> wrote:> Hi, > > It is known that time-varying may make an IIR unstable even it is > stable on its own. Imposing limits on the amount of varying is able to > eliminate this possibility of becoming unstable. > > I am wondering, is there a cookbook formula I can obtain these limits > on fc, Q or gain? > > Thanks a lot. > SYLSorry forget to mention, I am using DF1 with R B-J's cookbook formula.
Reply by ●October 28, 20082008-10-28
On Oct 28, 5:04 pm, SYL <sya...@gmail.com> wrote:> On Oct 28, 2:00 pm, SYL <sya...@gmail.com> wrote: > > > It is known that time-varying may make an IIR unstable even it is > > stable on its own. Imposing limits on the amount of varying is able to > > eliminate this possibility of becoming unstable. > > > I am wondering, is there a cookbook formula I can obtain these limits > > on fc, Q or gain?dunno about a cookbook, but Jean Laroche did a pretty good paper on the subject: On the Stability of Time-Varying Recursive Filters http://www.aes.org/e-lib/browse.cfm?elib=14168 i have it on paper, and i thought that since i was a member in 2007, i could get the pdf copy for free (that i could send you), but it doesn't seem like i can now. r b-j
Reply by ●October 29, 20082008-10-29
On 29 Oct, 10:00, SYL <sya...@gmail.com> wrote:> Hi, > > It is known that time-varying may make an IIR unstable even it is > stable on its own. Imposing limits on the amount of varying is able to > eliminate this possibility of becoming unstable. > > I am wondering, is there a cookbook formula I can obtain these limits > on fc, Q or gain? > > Thanks a lot. > SYLNot sure what you mean. Just work out its poles and make sure they are in the left hand plane (or within the unit circle). Time-varying or not the poles must lie there for it to be stable.
Reply by ●October 29, 20082008-10-29
robert bristow-johnson wrote:> >>>It is known that time-varying may make an IIR unstable even it is >>>stable on its own. Imposing limits on the amount of varying is able to >>>eliminate this possibility of becoming unstable. >> >>>I am wondering, is there a cookbook formula I can obtain these limits >>>on fc, Q or gain? > > > dunno about a cookbook, but Jean Laroche did a pretty good paper on > the subject:Is this about something similar to a parametric resonance, or just about the poles occasionally coming out of the unit circle while the coefficients are been modified? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 29, 20082008-10-29
Vladimir Vassilevsky wrote:> robert bristow-johnson wrote:>> dunno about a cookbook, but Jean Laroche did a pretty good >> paper on the subject:Kalinichenko's at DAFx '06 is also interesting and available, and ch. 6 of Clark's thesis provides little analysis but much data: http://www.dafx.ca/dafx06_proceedings.html (#57) http://www.tech.plym.ac.uk/spmc/rclark.html> Is this about something similar to a parametric resonance, or > just about the poles occasionally coming out of the unit circle > while the coefficients are been modified?Depending on the endpoint filters and transition method, formally stable intermediate coefficient sets may correspond to peaked response shapes so that the cumulative bound on state growth is finite but excessive. Martin -- Quidquid latine scriptum est, altum videtur.
Reply by ●October 29, 20082008-10-29
HardySpicer wrote:> On 29 Oct, 10:00, SYL <sya...@gmail.com> wrote: >> Hi, >> >> It is known that time-varying may make an IIR unstable even it is >> stable on its own. Imposing limits on the amount of varying is able to >> eliminate this possibility of becoming unstable. >> >> I am wondering, is there a cookbook formula I can obtain these limits >> on fc, Q or gain? >> >> Thanks a lot. >> SYL > > Not sure what you mean. Just work out its poles and make sure they are > in the left hand plane (or within the unit circle). > Time-varying or not the poles must lie there for it to be stable.Most time-varying filters are in transition, with the coefficients linearly interpolated between initial and final values. The end states being stable doesn't guarantee that intermediate states will also be stable. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 29, 20082008-10-29
Jerry Avins wrote:> HardySpicer wrote: > >> On 29 Oct, 10:00, SYL <sya...@gmail.com> wrote: >> >>> Hi, >>> >>> It is known that time-varying may make an IIR unstable even it is >>> stable on its own. Imposing limits on the amount of varying is able to >>> eliminate this possibility of becoming unstable. >>> >>> I am wondering, is there a cookbook formula I can obtain these limits >>> on fc, Q or gain? >>> >>> Thanks a lot. >>> SYL >> >> >> Not sure what you mean. Just work out its poles and make sure they are >> in the left hand plane (or within the unit circle). >> Time-varying or not the poles must lie there for it to be stable. > > > Most time-varying filters are in transition, with the coefficients > linearly interpolated between initial and final values. The end states > being stable doesn't guarantee that intermediate states will also be > stable.For the IIR filter of the second order, the linear transition of the coefficients guarantees that the intermediate states are always stable if the end points are stable. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 29, 20082008-10-29
Martin Eisenberg wrote:> Depending on the endpoint filters and transition method, formally > stable intermediate coefficient sets may correspond to peaked > response shapes so that the cumulative bound on state growth is > finite but excessive.For the filter of the N-th order, convert the denominator to the lattice structure and interpolate the parcors. The filter will be stable regardless of the transition curve. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 29, 20082008-10-29
On Oct 29, 10:14�am, Vladimir Vassilevsky <antispam_bo...@hotmail.com> wrote:> Jerry Avins wrote: > > HardySpicer wrote: > > >> On 29 Oct, 10:00, SYL <sya...@gmail.com> wrote: > > >>> It is known that time-varying may make an IIR unstable even it is > >>> stable on its own. Imposing limits on the amount of varying is able to > >>> eliminate this possibility of becoming unstable. > > >>> I am wondering, is there a cookbook formula I can obtain these limits > >>> on fc, Q or gain? > > > >> Not sure what you mean. Just work out its poles and make sure they are > >> in the left hand plane (or within the unit circle). > >> Time-varying or not the poles must lie there for it to be stable. > > > Most time-varying filters are in transition, with the coefficients > > linearly interpolated between initial and final values. The end states > > being stable doesn't guarantee that intermediate states will also be > > stable. > > For the IIR filter of the second order, the linear transition of the > coefficients guarantees that the intermediate states are always stable > if the end points are stable.sure, for 2nd-order filters with complex conjugate poles, the sqrt of the coef for the 2nd-order term (i call it "a2" but some old texts called it "b2") in the denominator is the distance the poles are from the origin (and -a1/2 is the real part of the two poles). as long as | a2| < 1, then supposedly the filter is stable. but you can have modulated parameters (e.g. a vibrato applied to the resonant frequency) where all of the instantaneous pole locations are all inside the unit circle, yet the filter blows up (if the modulation is large enough, fast enough, and the Q is high enough). that is what these papers cited (by me and Martin) are all about. r b-j
