matlab中画系统零极点的方法

写论文的时候由于需要画出系统的零极点图。但是之前不知道怎么用matlab画，今天研究了一下，拿出来和大家共享。所用到的matlab函数为zplane，matlab给出的解释如下：

     ZPLANE Z-plane zero-pole plot.
    ZPLANE(Z,P) plots the zeros Z and poles P (in column vectors) with the 
    unit circle for reference.  Each zero is represented with a 'o' and 
    each pole with a 'x' on the plot.  Multiple zeros and poles are 
    indicated by the multiplicity number shown to the upper right of the 
    zero or pole.  ZPLANE(Z,P) where Z and/or P is a matrix, plots the zeros
    or poles in different columns using the colors specified by the axes 
    ColorOrder property.
 
    ZPLANE(B,A) where B and A are row vectors containing transfer function
    polynomial coefficients plots the poles and zeros of B(z)/A(z).  Note
    that if B and A are both scalars they will be interpreted as Z and P.
 
    [HZ,HP,Hl] = ZPLANE(Z,P) returns vectors of handles to the lines and 
    text objects generated.  HZ is a vector of handles to the zeros lines, 
    HP is a vector of handles to the poles lines, and Hl is a vector of 
    handles to the axes / unit circle line and to text objects which are 
    present when there are multiple zeros or poles.  In case there are no 
    zeros or no poles, HZ or HP is set to the empty matrix [].
 
    ZPLANE(Z,P,AX) puts the plot into the axes specified by the handle AX.

      假设为一个零点，多个极点系统且b=[0.2 0.8 0.64],a=1,用zplane（b,a）就可以画出如下的系统零极点图。

       

     从图中可以看出。该系统有一个极点，两个零点，且都在单位圆以外，其中一个在单位圆附近，另一个距离单位圆较远。由于在单位圆外附近有零点存在，故该系统在某个频带有比较大的幅度衰落，相位特性也会成非线性。

     使用freqz函数可以画出系统的幅度特性和相位特性如下图所示

       可见在数字高频出，系统的幅度确实呈现大的衰减，相位变化也已经是非线性的了。

 

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