Publication detail

Analytical Solution of Non-Homogenous Difference Equation of 2nd order with Complex Conjugate Roots of Characteristic Equation

SMÉKAL, Z.

Original Title

Analytical Solution of Non-Homogenous Difference Equation of 2nd order with Complex Conjugate Roots of Characteristic Equation

English Title

Analytical Solution of Non-Homogenous Difference Equation of 2nd order with Complex Conjugate Roots of Characteristic Equation

Type

conference paper

Language

en

Original Abstract

Digital filters of the type of IIR are mostly realized as cascade or parallel connections of partial sections of 1st or 2nd order. In the design of the properties of partial sections we mostly start from the transfer function expressed in terms of the z-transform. The reason for the application of cascade or parallel connection of partial sections is the minimum sensitivity of frequency response to the quantization of system transfer function coefficients and inter-mediate results of arithmetic operations. In the implementation of digital filter in the digital signal processor, in particular in the simulation, we must often start from the solution of a linear non-homogeneous difference equation with constant coefficients that represents the properties of partial sections of digital filter. On these grounds it is of advantage to know a complete analytical solution of this difference equation.

English abstract

Digital filters of the type of IIR are mostly realized as cascade or parallel connections of partial sections of 1st or 2nd order. In the design of the properties of partial sections we mostly start from the transfer function expressed in terms of the z-transform. The reason for the application of cascade or parallel connection of partial sections is the minimum sensitivity of frequency response to the quantization of system transfer function coefficients and inter-mediate results of arithmetic operations. In the implementation of digital filter in the digital signal processor, in particular in the simulation, we must often start from the solution of a linear non-homogeneous difference equation with constant coefficients that represents the properties of partial sections of digital filter. On these grounds it is of advantage to know a complete analytical solution of this difference equation.

Keywords

Analytical Solution, Non-Homogeneous Difference Equations

Released

17.09.2004

Publisher

Dep. of Telecommunications, CUT Prague

Location

Prague

ISBN

80-01-03063-6

Book

Proc. of the Interantional Conference RTT2004

Edition number

1.vydání

Pages from

1

Pages to

4

Pages count

4

BibTex


@inproceedings{BUT11468,
  author="Zdeněk {Smékal}",
  title="Analytical Solution of Non-Homogenous Difference Equation of 2nd order with Complex Conjugate Roots of Characteristic Equation",
  annote="Digital filters of the type of IIR are mostly realized as cascade or parallel connections of partial sections of 1st or 2nd order. In the design of the properties of partial sections we mostly start from the transfer function expressed in terms of the z-transform. The reason for the application of cascade or parallel connection of partial sections is the minimum sensitivity of frequency response to the quantization of system transfer function coefficients and inter-mediate results of arithmetic operations. In the implementation of digital filter in the digital signal processor, in particular in the simulation, we must often start from the solution of a linear non-homogeneous difference equation with constant coefficients that represents the properties of partial sections of digital filter. On these grounds it is of advantage to know a complete analytical solution of this difference equation.",
  address="Dep. of Telecommunications, CUT  Prague",
  booktitle="Proc. of the Interantional Conference RTT2004",
  chapter="11468",
  institution="Dep. of Telecommunications, CUT  Prague",
  year="2004",
  month="september",
  pages="1",
  publisher="Dep. of Telecommunications, CUT  Prague",
  type="conference paper"
}