~ubuntu-branches/ubuntu/hoary/scilab/hoary

<SP>: real vector or polynomial in <VERB>z^-1</VERB>, it contains the coefficients of the Fourier's series of the rational system to approximate (the impulse response)</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>den0</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: a polynomial which gives an initial guess of the solution, it may be <VERB>poly(1,'z','c')</VERB></SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>n</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: integer, the degree of approximating transfer function (degree of den)</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>imp</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: integer in <VERB>(0,1,2)</VERB> (verbose mode)</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>h</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: transfer function <VERB>num/den</VERB> or transfer matrix (column vector) when flag <VERB>'all'</VERB> is given.</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>den</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: polynomial or vector of polynomials, contains the denominator(s) of the solution(s)</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>num</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: polynomial or vector of polynomials, contains the numerator(s) of the solution(s)</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

<PARAM_ITEM>

<PARAM_NAME>err</PARAM_NAME>

<PARAM_DESCRIPTION>

<SP>: real constant or vector , the l2-error achieved for each solutions</SP>

</PARAM_DESCRIPTION>

</PARAM_ITEM>

</PARAM_INDENT>

</PARAM>

<VERB>[den,num,err]=arl2(y,den0,n [,imp]) </VERB> finds a pair of polynomials

<VERB>num</VERB> and <VERB>den</VERB> such that the transfer function <VERB>num/den</VERB>

is stable and its impulse response approximates (with a minimal l2

norm) the vector <VERB>y</VERB> assumed to be completed by an infinite number

of zeros.

If y(z) = y(1)(1/z)+y(2)(1/z^2)+ ...+ y(ny)(1/z^ny)

then l2-norm of <VERB>num/den - y(z)</VERB> is <VERB>err</VERB>.

<VERB>n</VERB> is the degree of the polynomial <VERB>den</VERB>.

The <VERB>num/den</VERB> transfer function is a L2 approximant of the

Fourier's series of the rational system.

Various intermediate results are printed according to <VERB>imp</VERB>.

<VERB>[den,num,err]=arl2(y,den0,n [,imp],'all') </VERB> returns in the

vectors of polynomials <VERB>num</VERB> and <VERB>den</VERB> a set of local

optimums for the problem. The solutions are sorted with increasing

errors <VERB>err</VERB>. In this case <VERB>den0</VERB> is already assumed to be

</DESCRIPTION>

<![CDATA[

v=ones(1,20);

xbasc();

plot2d1('enn',0,[v';zeros(80,1)],2,'051',' ',[1,-0.5,100,1.5])

[d,n,e]=arl2(v,poly(1,'z','c'),1)

plot2d1('enn',0,ldiv(n,d,100),2,'000')

[d,n,e]=arl2(v,d,3)

plot2d1('enn',0,ldiv(n,d,100),3,'000')

[d,n,e]=arl2(v,d,8)

100

plot2d1('enn',0,ldiv(n,d,100),5,'000')

101

102

[d,n,e]=arl2(v,poly(1,'z','c'),4,'all')

103

plot2d1('enn',0,ldiv(n(1),d(1),100),10,'000')

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]]>

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</EXAMPLE>

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<SEE_ALSO>

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<SEE_ALSO_ITEM>

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</SEE_ALSO_ITEM>

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<SEE_ALSO_ITEM>

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<LINK>imrep2ss</LINK>

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</SEE_ALSO_ITEM>

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<SEE_ALSO_ITEM>

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</SEE_ALSO_ITEM>

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<SEE_ALSO_ITEM>

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<LINK>armax</LINK>

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</SEE_ALSO_ITEM>

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<SEE_ALSO_ITEM>

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</SEE_ALSO_ITEM>

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</SEE_ALSO>

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</MAN>

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