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State-space formulation of lattice-ladder filter

Started by Thomas Arildsen June 23, 2009
As I understand it, an ARMA system can be realized as a lattice/ladder 
filter (e.g. Matlab: tf2latc). In "EFFICIENT ALGORITHM FOR ADAPTIVE 
NORMALISED LATTICE FILTERS" by Nguyen, 1983 (found on IEEExplore), there 
is a state-space formulation of a lattice filter.
Does anyone know of a state-space formulation of a lattice/ladder filter?

Thomas Arildsen
-- 
Al email til afsenderadressen går tabt.
Min rigtige adresse er hos arildsen dot org til brugeren thomas.
Thomas Arildsen wrote:

> As I understand it, an ARMA system can be realized as a > lattice/ladder filter (e.g. Matlab: tf2latc). In "EFFICIENT > ALGORITHM FOR ADAPTIVE NORMALISED LATTICE FILTERS" by Nguyen, > 1983 (found on IEEExplore), there is a state-space formulation > of a lattice filter. Does anyone know of a state-space > formulation of a lattice/ladder filter?
It should be the same as the lattice formulation except for the state-to-output matrix which, instead of having just a single nonzero entry, becomes the row vector of ladder coefficients. This is of course speaking with respect to the flowgraph form with the ladder on the output side. In the transposed form you would replace the input-to-state matrix accordingly. Martin -- Quidquid latine scriptum est, altum videtur.
On Tue, 23 Jun 2009 17:48:13 +0000, Thomas Arildsen wrote:

> As I understand it, an ARMA system can be realized as a lattice/ladder > filter (e.g. Matlab: tf2latc). In "EFFICIENT ALGORITHM FOR ADAPTIVE > NORMALISED LATTICE FILTERS" by Nguyen, 1983 (found on IEEExplore), there > is a state-space formulation of a lattice filter. Does anyone know of a > state-space formulation of a lattice/ladder filter? > > Thomas Arildsen
Does the article not have a block diagram? Can you not just translate it into state space form by inspection? -- www.wescottdesign.com
Den Tue, 23 Jun 2009 18:20:06 +0000 skrev Martin Eisenberg:

> Thomas Arildsen wrote: > >> As I understand it, an ARMA system can be realized as a lattice/ladder >> filter (e.g. Matlab: tf2latc). In "EFFICIENT ALGORITHM FOR ADAPTIVE >> NORMALISED LATTICE FILTERS" by Nguyen, 1983 (found on IEEExplore), >> there is a state-space formulation of a lattice filter. Does anyone >> know of a state-space formulation of a lattice/ladder filter? > > It should be the same as the lattice formulation except for the > state-to-output matrix which, instead of having just a single nonzero > entry, becomes the row vector of ladder coefficients. > > This is of course speaking with respect to the flowgraph form with the > ladder on the output side. In the transposed form you would replace the > input-to-state matrix accordingly.
Well, then I think the structure _is_ actually a lattice/ladder filter. On closer examination it does have a ladder output stage and an output vector containing the tap weights. I am not very familiar with lattice(/ladder) filters and was a little thrown off by the fact the author just calls it a lattice filter. Thanks, Thomas Arildsen -- Al email til afsenderadressen går tabt. Min rigtige adresse er hos arildsen dot org til brugeren thomas.
Den Tue, 23 Jun 2009 13:44:41 -0500 skrev Tim Wescott:

> On Tue, 23 Jun 2009 17:48:13 +0000, Thomas Arildsen wrote: > >> As I understand it, an ARMA system can be realized as a lattice/ladder >> filter (e.g. Matlab: tf2latc). In "EFFICIENT ALGORITHM FOR ADAPTIVE >> NORMALISED LATTICE FILTERS" by Nguyen, 1983 (found on IEEExplore), >> there is a state-space formulation of a lattice filter. Does anyone >> know of a state-space formulation of a lattice/ladder filter? >> >> Thomas Arildsen > > Does the article not have a block diagram? Can you not just translate > it into state space form by inspection?
As I wrote in my reply to Martin Eisenberg, I think the filter in question is actually a lattice/ladder filter, so the state-space model does apply after all. I was trying to construct the state-space representation myself, but there would be no need to if there was a well- known answer to the problem already. Best regards, Thomas Arildsen -- Al email til afsenderadressen går tabt. Min rigtige adresse er hos arildsen dot org til brugeren thomas.