IMPLEMENTATION OF SYSTEMSC. Williams & W. AlexanderNorth Carolina State University, Raleigh, NC (USA)ECE 513, Fall 2017C. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20171 / 214
Outline1Introduction2Structures for FIR SystemsDirect–Form StructuresCascade-Form StructuresPolyphase FIR Filter RealizationLinear Phase FIR Filter3FIR Second Order Sections4FIR Lattice Structure5Structures for IIR SystemsDirect Form StructureTranspose Direct Form StructureCascade–Form Structures6IIR SOS from Difference Equation7Parallel IIR Form8All Pass Digital Filters9All Pole IIR Lattice Structure[?]10IIR Lattice Structure11The Linear Phase IIR Filter[?]12ReferencesC. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20172 / 214
IntroductionWe consider the realization of linear, shift–invariant, discrete–timesystems in this Chapter.We will:Develop computational structure for various linear, shift–invariant,discrete–time systems.Develop one or more difference equations that can be used tocompute the output sequence for an arbitrary input sequence forthe linear, shift–invariant, discrete–time system.C. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20173 / 214
IntroductionC. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20174 / 214
C. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20175 / 214
IntroductionC. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20176 / 214
IntroductionTherefore, it is of interest to consider the alternate forms for therealization of digital filters.We consider the different realizations for discrete–time systems inthis Chapter.C. Williams & W. Alexander (NCSU)IMPLEMENTATION OF SYSTEMSECE 513, Fall 20177 / 214
Structures for FIR SystemsIn general, a FIR system can be described by a finite differenceequation that involves only inputs and no previous outputs tocompute the output.