3
$\begingroup$

In papers and textbooks and on Wikipedia, I regularly stumble upon so-called "lattice filters". They always look horribly more complex than their 'non-lattice counterpart' and I usually don't really understand what's going on (and why). I could not really find a useful introduction to lattice filters and the fundamental idea behind them. What I believe to have understood (please correct me if I'm wrong) is that they represent some form of very efficient implementation scheme for classical filters, e.g., RLS?

Can somebody explain the intuition behind lattice filters? What are they, which problem do they solve, and how do they solve it? References to readable introductions are also highly appreciated.

(Note that I have actually had a fair amount of DSP in my undergrad studies, but lattice filters were never even mentioned.)

$\endgroup$
2
  • 1
    $\begingroup$ Do you have Oppenheim and Schafer, Discrete-Time Signal Processing? $\endgroup$ Apr 21, 2021 at 18:32
  • 1
    $\begingroup$ Thanks, those are both very helpful suggestions! After skimming the relevant chapter (Structures for Discrete-Time Systems) of Oppenheim / Schafer, I now have at least a rough understanding of what's going on. It's interesting to note that Oppenheim / Schafer mostly emphasize the increased numerical precision, whereas one important claim on the RLS wiki page is that the lattice algorithm has lower computational complexity. That result may be very specific for the RLS lattice algorithm that is mentioned there, though. $\endgroup$
    – Eike P.
    Apr 23, 2021 at 10:55

1 Answer 1

1
$\begingroup$

The intuition behind lattice filters probably is connected with the propagation of waves and modeling wave propagation with discrete cells.

$\endgroup$
3
  • 1
    $\begingroup$ Can you elaborate? $\endgroup$
    – ecook
    Mar 7, 2022 at 5:18
  • 1
    $\begingroup$ Each section of the Lattice Filter has two signals, one that inputs from the left and outputs to the right, and another in the opposite direction. And there is one memory state in each section. You can think of a chain of many of these sections, connected left to right, as a discrete simulation of a wave propagation in both the left and right directions. $\endgroup$ Mar 7, 2022 at 5:47
  • $\begingroup$ This is the intuition that is taught in acoustics oriented education as I recall. A set of uniform tubes (eg your throat). $\endgroup$
    – Knut Inge
    May 18, 2022 at 18:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.