MGTcoefficientsai2bi

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Auxiliary function
Introduced first in SolidGeometry 5.0, Creation date: 2021-02-11, Last change: 2025-09-15

converts a z-transform Denominator polynomial into Numerator polynomial



See Also: MGTsystemFIR , MGTsystemIIR , MGTsysteminvFIR , MGTcontrolIIRIIR , MGTcoefficientsPID2bi

Example Illustration

missing image of MGTcoefficientsai2bi(ai,thr)

Syntax

[bi,cbi]=MGTcoefficientsai2bi([ai,thr])

Input Parameter

ai: ai coefficients of a strucuture of type 1/ai polynomial
thr: default is 1e-3

Output Parameter

bi: ai coefficients of an equivalent strucuture of type bi polynomial
cbi:

Examples


ai=[1.2 -0.3 0.1]
[bi,cbi]=MGTcoefficientsai2bi(ai)



Copyright 2021-2025 Tim C. Lueth. All rights reserved. The code is the property of Tim C. Lueth and may not be redistributed or modified without explicit written permission. This software may be used free of charge for academic research and teaching purposes only. Commercial use, redistribution, modification, or reverse engineering is strictly prohibited. Access to source code is restricted and granted only under specific agreements. For licensing inquiries or commercial use, please contact: Tim C. Lueth

Algorithm (Workflow)

This function, MGTcoefficientsai2bi, converts a z-transform denominator polynomial into a numerator polynomial. It is part of the SG-Library and was introduced in SolidGeometry 5.0.

Input Parameters

Output Results

Algorithm Steps

  1. Retrieve the ai coefficients and thr threshold from the input parameters using getfuncparams.
  2. Set nmax to 32, which is the maximum number of coefficients.
  3. Initialize an impulse response array, Impulse, with zeros and set the first element to 1.
  4. Calculate the bi coefficients using the MGTsystemIIR function with the impulse response and ai coefficients.
  5. Find the indices of bi where the absolute value is greater than thr and store the last index in l.
  6. If l equals nmax, issue a warning that the number of coefficients may be too small.
  7. Trim the bi array to the first l elements.
  8. Calculate the damping factor, damp, as the sum of the bi coefficients.
  9. Compute cbi as the difference between bi and its shifted version.
  10. If no output is requested, print the ai and bi coefficients, the damping factor, and plot the bi coefficients using PLplotdiscretetime.
Algorithm explaination created using ChatGPT on 2025-08-19 08:02. (Please note: No guarantee for the correctness of this explanation)

Last html export of this page out of FM database by TL: 2025-09-21