Thu Apr 18 13:36:56 EDT 2013

Lattice, Ladder and Waveguide

Since all these concepts are related, it is hard to get subjective and
pick out the most important concept.  We might choose the central idea
to be the construction of a family of allpass filters from a single
recursion relation that corresponds directly to the structural
operation of adding a left/right signal flow section to an existing
allpole filter.

The normalized ladder filter can be interpreted as a time--shifted
version of a lossless digital waveguide.  This analogy can be used to
add a physical interpretation to the resulting structure.

Once an allpass filter is obtained from the iterative construction
process, the allpole filter corresponding to the denominator of the
allpass is accessible directly in the filter structure, and the two
FIR filters that make up the numerator and denominator of the allpass
are accessible in the time--reversed ladder filter.

From the time--reversed normalized ladder filter, the lattice filter
can be constructed by dropping the normalizing multiplication between
different sections.  This structure is the same as the one can be
derived from the Levinson-Durbin algorithm for solving the Yule-Walker
equations occuring in the problems of autoregressive modeling and
linear prediction.

To realize an arbitrary minimim phase FIR, allpole or stable allpass,
any of the structures can be used.

As a remaining question, why would one use a normalized ladder filter
instead of an IIR lattice filter (non-normalized ladder) in the
construction of an allpass filter?