readme.txt

对输入的一有理Z变换表达式（输入分子和分母系数序列）

功能：
对输入的一有理Z变换表达式（输入分子和分母系数序列），分别画出：
（1）零极点图
（2）z在单位圆上时z变换所对应的DTFT的幅度谱和相位谱
（3）逆z变换所得序列，在各种不同的收敛域下

 
1. Structure of the program:
   程序入口与界面控制在 Homework3.m 与 Homework3.fig中，其中也包含了计算与画图的代码
   InvZTrans.m中实现了一个同名函数，作用是根据z-transform function 和 ROC来计算对应的序列。
   ROCFactor.m中的同名函数的作用是：根据ROC将有理分式分解为两部分，其中一部分对应了左边序列，另一部分对应了右边序列。
  
2. An example to use this utility
Use the default input data in the interface. That is: 
Coefficients for Numberator: 2 -2.5
Coefficients for Denominator: 1 -2.5 1
Press the button labeled "Cofficients OK"，then a zero will be pedded at the end of numberators, and the transform function, (2z^2 - 2.5z)/(z^2 -2.5z +1), will be showed in the right rectangle. 

Next, pls press the button labeled "calculate zero,pole points", then the zero&pole plot will be displayed.

此时，listbox中默认选择ROC为|z|<0.5, 则此时单位圆不在ROC内，"Draw mag&phase map"按钮disable. 按下"Do inverse z-transform"按钮, 一个左边序列将显示在图中。（如果想知道序列上各点的值，可以选中界面右上角的"also output the result to console", 然后再按"Do inverse z-transform"按钮，则可以在command window中看到序列上各点的值）

如果在listbox中选择ROC为0.5<|z|<2,则"Draw mag&phase map"按钮enable, 按下该键可以看到Magnitude Spectrum 和Phase Spectrum. 按下"Do inverse z-transform"按钮, 一个双边序列将显示在图中。

如果在listbox中选择ROC为2<|z|,则"Draw mag&phase map"按钮disable. 按下"Do inverse z-transform"按钮, 一个右边序列将显示在图中。

3. Manual
----Initial State---
Only the two editbox for inputing coefficients and the botton labled "coefficients OK" are enabled.
 
----STEP 1---- 
<Operation>: 
    a. Input the coefficients for both numberator and denominator
    b. Click the button labeled 'Cofficients OK'. 
<Expected result>:
    a. These two coefficients vector will be forced to the same length by appending zeros, and the transform function will be printed at the right box. 
    b. The button labeled "calculate zero, pole points" will be enabled. 
<Note>:
    a. Denominator must have non-zero leading coefficient.
    b. Denominator cannot be zero or empty.

----STEP 2-----
<Operation>:
    a. Click the button labeled "calculate zero, pole points".
<Expected result>:
    a. The Z-plane zero-pole plot will be showed.
    b. The listbox labeled "Please select ROC" will be enabled. 

----STEP 3-----
<Operation>:
    a. Select a ROC from the listbox labled "Please select ROC".
<Expected result>:
    a. If the ROC you selected includs unit circle, the button labeled "Draw mag&phase map" will be enabled.
    b. The button labeled "Do inverse z-transform" will be enabled. 

----STEP 4----
<Operation>:
    a. If the button labeled "Draw mag&phase map" is enabled, click it.
<Expected result>:
    a. The magnitude and pahse map on unit circle will be showed.
<Note>:
    a. Before getting the two map, you can input the number of frequency points by yourself, or just take the default value, 256.

----STEP 5----
<Operation>:
    a. Click the button labeled "Do inverse z-transform".
<Expected result>:
    a. The seqence generated by inverse Z transform will be showed.
<Note>:
    a. You can choose the length of ouput sequence, or you can let the function, impz, to decide how many points will be showed.  

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为了使用方便，在界面右上方设立了一个选项--"also output the result to cosole", 如果希望在控制台看到计算结果的数字值，可以选中该项。