This is a pseudo-mirror of www.bores.com DSP intro at http://www.bores.com/courses/intro/iir/5_transp.htm [sic] as per the policy of this site.
This mirror was created from the source on 03/08/2000 at 22:46 Central Time.
Commercial information, time-dependent information, and all the damn JAVA scripts have been removed.  All "htm" extensions have been changed to the proper "html" extensions.  Has also been edited for coherence, proper-linkage, and better document flow.
Copied without permission.

Introduction to DSP

IIR filters

Direct form II

The transposition theorem says that if we take a filter diagram and reverse all the elements - swapping the order of execution for every element, and reversing the direction of all the flow arrows - then the result is the same:

• if everything is turned back to front, it all works just the same

This means that the direct form 1 diagram can be obtained by transposition of the direct form 2 diagram:

For this reason, direct form 1 is often called transposed direct form 2.

Don't ask me why these terms seem to be as confusing as they possibly could be - I didn't make them up. I imagine mathematicians sit around at coffee break and come up with new ways to spread despondency amongst us lesser mortals. Here are the two main sources of confusion:

direct form 1

so called because it can be drawn direct from the filter equation

direct form 2

so called because it can be derived by changing the diagram of direct form 1

transposed

so called because it is obtained by transposition of direct form 2 - but really, this is just direct form 1

canonic

so called because it has the minimum number of delay elements - but really, it is just direct form 2

| Last updated: 4th January 1998 | http://www.bores.com/courses/intro/iir/5_transp.htm

Telephone: 01483 740138 fax: 01483 740136 email:  Web: http://www.bores.com