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===Other forms=== {{prose|section|date=April 2025}} Other forms include: * Direct form I and II transpose * Series/cascade lower (typical second) order subsections * Parallel lower (typical second) order subsections ** Continued fraction expansion * Lattice and ladder ** One, two and three-multiply lattice forms ** Three and four-multiply normalized ladder forms ** ARMA structures * State-space structures: ** optimal (in the minimum noise sense): <math>(N+1)^2</math> parameters ** block-optimal and section-optimal: <math>4N-1</math> parameters ** input balanced with Givens rotation: <math>4N-1</math> parameters<ref name=LMXH10>{{cite journal|last=Li|first=Gang|author2=Limin Meng |author3=Zhijiang Xu |author4=Jingyu Hua |title=A novel digital filter structure with minimum roundoff noise|journal=Digital Signal Processing|date=July 2010|volume=20|issue=4|pages=1000–1009|doi=10.1016/j.dsp.2009.10.018|bibcode=2010DSP....20.1000L }}</ref> * Coupled forms: Gold Rader (normal), State Variable (Chamberlin), Kingsbury, Modified State Variable, Zölzer, Modified Zölzer * Wave Digital Filters (WDF)<ref name=Fet86>{{cite journal|last=Fettweis|first=Alfred|title=Wave digital filters: Theory and practice|journal=Proceedings of the IEEE|date=Feb 1986|volume=74|issue=2|pages=270–327|doi=10.1109/proc.1986.13458|s2cid=46094699}}</ref> * Agarwal–Burrus (1AB and 2AB) * Harris–Brooking * ND-TDL * Multifeedback * Analog-inspired forms such as Sallen-key and state variable filters * [[Systolic array]]s
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