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Impulse response invariant discretization of fractional order low-pass filters

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Impulse response invariant discretization of fractional order low-pass filters

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07 Sep 2008 (Updated )

Discretize [1/(\tau s +1)]^r with "r" a real number

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Description

% Impulse response invariant discretization of fractional order
% low-pass filters
%
% irid_folpf function is prepared to compute a discrete-time finite
% dimensional (z) transfer function to approximate a continuous-time
% fractional order low-pass filter (LPF) [1/(\tau s +1)]^r, where "s" is
% the Laplace transform variable, and "r" is a real number in the range of
% (0,1), \tau is the time constant of LPF [1/(\tau s +1)].
%
% The proposed approximation keeps the impulse response "invariant"
%
% IN:
% tau: the time constant of (the first order) LPF
% r: the fractional order \in (0,1)
% Ts: the sampling period
% norder: the finite order of the approximate z-transfer function
% (the orders of denominator and numerator z-polynomial are the same)
% OUT:
% sr: returns the LTI object that approximates the [1/(\tau s +1)]^r
% in the sense of invariant impulse response.
% TEST CODE
% dfod=irid_folpf(.01,0.5,.001,5);figure;pzmap(dfod)
%
% Reference: YangQuan Chen. "Impulse-invariant discretization of fractional
% order low-pass filters".
% Sept. 2008. CSOIS AFC (Applied Fractional Calculus) Seminar.
% http://fractionalcalculus.googlepages.com/
% --------------------------------------------------------------------
% YangQuan Chen, Ph.D, Associate Professor and Graduate Coordinator
% Department of Electrical and Computer Engineering,
% Director, Center for Self-Organizing and Intelligent Systems (CSOIS)
% Utah State University, 4120 Old Main Hill, Logan, UT 84322-4120, USA
% E: yqchen@ece.usu.edu or yqchen@ieee.org, T/F: 1(435)797-0148/3054;
% W: http://www.csois.usu.edu or http://yangquan.chen.googlepages.com
% --------------------------------------------------------------------
%
% 9/7/2009
% Only supports when r in (0,1). That is fractional order low pass filter.
% HOWEVER, if r is in (-1,0), we call this is a "fractional order
% (proportional and derivative controller)" - we call it FO(PD).
% Note: it may be needed to make FO-LPF discretization minimum phase first.
%
% See also irid_fod.m
% at http://www.mathworks.com/matlabcentral/files/21342/irid_fod.m
% See also srid_fod.m
% (See how the nonminimum phase zeros are handled)
% See also gml_fun.m
% at http://www.mathworks.com/matlabcentral/files/20849/gml_fun.m

Acknowledgements

Generalized Mittag Leffler Function and Impulse Response Invariant Discretization Of Fractional Order Integrators/Differentiators inspired this file.

Required Products Signal Processing Toolbox
Control System Toolbox
MATLAB release MATLAB 7.4 (R2007a)
Other requirements Need the following to run: % See also gml_fun.m % at http://www.mathworks.com/matlabcentral/files/20849/gml_fun.m
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21 Oct 2013 luluweijia  

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