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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
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<LANGUAGE>eng</LANGUAGE>
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<TYPE>Scilab Function</TYPE>
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<DATE>April 1993</DATE>
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<SHORT_DESCRIPTION name="freq"> frequency response</SHORT_DESCRIPTION>
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<CALLING_SEQUENCE_ITEM>[x]=freq(A,B,C [,D],f) </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM>[x]=freq(NUM,DEN,f) </CALLING_SEQUENCE_ITEM>
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<PARAM_NAME>A, B, C, D</PARAM_NAME>
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<SP>: real matrices of respective dimensions <VERB>nxn, nxp, mxn, mxp</VERB>.</SP>
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<PARAM_NAME>NUM,DEN</PARAM_NAME>
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<SP>: polynomial matrices of dimension <VERB>mxp</VERB></SP>
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<PARAM_NAME>x</PARAM_NAME>
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<SP>: real or complex matrix</SP>
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<P><VERB>x=freq(A,B,C [,D],f)</VERB> returns a real or complex <VERB>mxp*t</VERB> matrix
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<P><VERB>x(:,k*p:(k+1)*p)= C*inv(f(k)*eye()-A)*B + D</VERB>.</P>
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Thus, for <VERB>f</VERB> taking values along the imaginary axis or
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on the unit circle <VERB>x</VERB> is the continuous or discrete time
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frequency response of <VERB>(A,B,C,D)</VERB>.</P>
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<P><VERB>x=freq(NUM,DEN,f)</VERB> returns a real or complex matrix <VERB>x</VERB> such
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that columns <VERB>k*(p-1)+1</VERB> to <VERB>k*p</VERB> of <VERB>x</VERB> contain the matrix
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<VERB>NUM(f(k))./DEN(f(k))</VERB></P>
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rep=freq(sys("num"),sys("den"),[0,0.9,1.1,2,3,10,20])
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[horner(sys,0),horner(sys,20)]
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freq(A,B,C,[0,0.9,1.1,2,3,10,20])