matlab中画系统零极点的方法

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。