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Chapter 6  z Transforms

 

 

 

Inverse Z Transform Z反变换

 

 

 

Long Division Method长除法

 

 

 

Partial Fraction Expansion

        部分因式展开

 

H

 

 

 

 

 

 

 

Homework: p223: 6.7 

                     p224:6.16

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Inverse Z Transform Z反变换

 

     Definition定义

 

 

 

 

     Computation Methods求解方法

                    

         1. Eye Matching观察法

X(z) 1

 

 

 

x[n] d [n] u [n] bn u[n] n u[n]

          Page 188: Example 6.23

 

         2. Impulse Function Method冲激函数法

                     Knowing:     Z-1{ z -k } = d [ n-k ]

Goal:        

               

                                                        

         3. Step Function Method阶跃函数法

Knowing:

 

 

Goal:

               

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Long Division Method长除法

 

     Standard Form标准型

                        

 

 

            Numerator分子and Denominator分母

          are not always of same order,

          because it is often that MN .

 

 

 

     Long Division长除法

 

              How many denominators分母

           are there in the numerator分子.

 

Goal:

       

 

                       P189 eg.6.25

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Partial Fraction Expansion

           部分因式分解

 

 

For given

                      
 

 

Let

 

 

 

 

 

         Thus from {ak , bk , fn(β), gn(α, β)},

               α and β are solvable可解.

 

                 Skills are more helpful!

 

                                              P193 eg.6.28