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Diffstat (limited to 'help/en_US/levinson.xml')
-rw-r--r-- | help/en_US/levinson.xml | 76 |
1 files changed, 1 insertions, 75 deletions
diff --git a/help/en_US/levinson.xml b/help/en_US/levinson.xml index ac340a6..056795f 100644 --- a/help/en_US/levinson.xml +++ b/help/en_US/levinson.xml @@ -17,81 +17,7 @@ <refnamediv> <refname>levinson</refname> - <refpurpose>Levinson-Durbin Recurssion Algorithm</refpurpose> - <para> </para> + <refpurpose></refpurpose> </refnamediv> - -<refsynopsisdiv> - <title>Calling Sequence</title> - <synopsis> -a = levinson(r) -a = levinson(r,n) -[a,e] = levinson(r,n) -[a,e,k] = levinson(r,n) - </synopsis> - <para> </para> -</refsynopsisdiv> - -<refsection> - <title>Parameters</title> - <variablelist> - <varlistentry><term>r</term> - <listitem><para> Real or complex deterministic autocorrelation sequence input </para></listitem></varlistentry> - <varlistentry><term>a</term> - <listitem><para> Coefficients of length(r)-1 order Autoregressive linear process </para></listitem></varlistentry> - <varlistentry><term>n</term> - <listitem><para> Order of autoregressive model (default value is length(r)-1 , if n is not given)</para></listitem></varlistentry> - <varlistentry><term>e</term> - <listitem><para> Prediction error of order n</para></listitem></varlistentry> - <varlistentry><term>k</term> - <listitem><para> Reflection coefficient vector of length n</para></listitem></varlistentry> - </variablelist> - <para> </para> -</refsection> - -<refsection> - <title>Description</title> - <para> The Levinson-Durbin recursion algorithm is used for finding an all-pole IIR filter with a given deterministic autocorrelation sequence (r) </para> - - <para> - <latex> - \begin{eqnarray} - H(z) = \frac{1}{1+a(2)z^{-1}+a(3)z^{-2} + ... +a(n+1)z^{-n}} - \end{eqnarray} - </latex> - </para> - - <para> </para> -</refsection> - -<refsection> - <title>Examples </title> - <para> Estimate the coefficients of an autoregressive process given by equation </para> - - <para> - <latex> - \begin{eqnarray} - x(n) = 0.1x(n-1) - 0.8x(n-2) + w(n) - \end{eqnarray} - </latex> - </para> - <para> </para> - - <programlisting role="example"><![CDATA[ - -a = [1 0.1 -0.8]; - -v = 0.4; //variance, v=0.4 -w = sqrt(v)*rand(15000,1,"normal"); -x = filter(1,a,w); - -[r,lg] = xcorr(x,'biased'); -r(lg<0) = []; - -ar = levinson(r,length(a)-1) //coefficients of autoregressive process - -]]></programlisting> -</refsection> - </refentry> |