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第十章 离散时间系统及卷积 PowerPoint PPT Presentation


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第十章 离散时间系统及卷积. 10.1 离散时间系统. 输入 si(n). 输出 so(n). 系统. 1 、离散系统的概念. 离散时间系统是指输入及输出信号均是离散信号的系统。. 系统 1. 输入. 输入. 输出. 系统 1. 系统 2. 系统 2. 系统 1. 系统 2. 输出. 输入. 系统 4. 系统 3. 2 、离散系统的互联. 输出. a. 系统的级联. b. 系统的并联. c. 系统的混联. 3 、离散时间系统的模型. 10.2 离散时间系统的分类. 1 、线性系统. 2 、时不变系统. 3 、因果系统.

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第十章 离散时间系统及卷积

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10.1


si(n)

so(n)

1


1

1

2

2

1

2

4

3

2

a.

b.

c.


3


10.2


1


2


3


4


10.3


1

  • h(t)h(n)


2


3

h(n)

(n)

n

n

f(n)

T


s(t)

f(t)

h(n)f(0)

t

T

h(n-1)f(1)

f(n)h(n)

t

h(n-k)f(k)

t


  • -


4

  • s(n)h(n)= h(n) s(n)

  • s(n)[h1(n)+h2(n)]= s(n) h1(n)+ s(t) h2(n)


5


  • h(n)=(n)


10.4


1

1

2

h1(n)

h2(n)

h(n)

h(n)=h1(n)h2(n)


2

1

h1(n)

2

h2(n)

h(n)

h(n)=h1(n)+h2(n)


1

2

4

3

h(t)

3

h1(t)

h2(t)

h4(t)

h3(t)

h(t)={[h1(t)h2(t)]+ h3(t)} h4(t)


10.5


1



1

1

2

h1(n)

h2(n)

h(n)

h(n)=h1(n)h2(n)H()=H1()H2()


2

1

h1(n)

2

h2(n)

h(n)

h(n)=h1(n)+h2(n) H()=H1()+H2()


1

2

4

3

h(n)

3

h1(n)

h2(n)

h4(n)

h3(n)

h(n)={[h1(n)h2(n)]+ h3(n)} h4(n)

H()={H1()H2()+H3()} H4()


2




si(0)=2h(n)

si(n)

3

4

2

2

2

n

si(0)

si(1)

n

h(n)

si(1)=3h(n-1)

2

1

1

6

n

3

3

n

=2h(n)+3h(n-1)

8

7

3

2

n


3

  • h(n)


10.6


  • H()h(n)


10.7 DFT


1

  • x(n)n=0,1,2,N-1<x(n-k)>N

<X(n-1)>N

<X(n-2)>N

X(n)

3

n

3

n

3

n

<X(n-4)>N

<X(n-3)>N

3

n

3

n


2

  • x(n)h(n)y(n)Y()=X()H()y(n)

  • Y(k)y(n)


  • FFTIFFT

  • x(n)h(n)n[0,N)(DFT)X(k)H(k) k[0,N)

  • Y(k)=X(k)H(k)

  • Y(k)(IDFT)y(n)


h(n)

3

n

3

n

n

3

[0,N-1]=

<h(n-1)>N

3

n


n

3

n

3

n

n

3

3

[0,N-1]=

<h(n-2)>N

[0,N-1]=

<h(n-m)>N


  • Kh(n)Lx(n)y(n)

  • K+L-1


h(n)=[1,2,3,4]

h(0-m)

3

n

3

m

x(n)=[1,2,2,1]

x(m)

3

n

3

m


h(1-m)

3

m

x(m)

3

m


  • y(n)=[1,4,9,15,16,11,4]7


<h(0-m)>N

3

m

x(m)

3

m


  • <h(0-m)>N

h(m)

<h(0-m)>N

<h(n-m)>N

3

m

<h(0-m)>N

h(-m)

0~N-1

3

m

3

m

3

m


<h(1-m)>N

3

m

x(m)

3

m


  • y(n)=[17,15,13,15]y(n)

  • y(n)=y(n)??

  • Kx(n)Lh(n)0K+L-1


h(n)=[1,2,3,4,0,0,0]

0

7

n

x(n)=[1,2,2,1, 0,0,0]

7

n


<h(0-m)>N

7

m

x(m)

<h(0-m)>N

7

m


<h(1-m)>N

7

m

x(m)

7

m


  • y(n)=[1,4,9,15,16,11,4]=y(n)

  • Kx(n)Lh(n)K+L-1

    X(k)H(k)

    X(k)H(k)Y(k)

    Y(k)y(n)


  • K+L-12MK+L-1K+L-122K+L-1

  • FFTIFFT


Kx(n)Lh(n)K+L-12M

FFTX(k)H(k)

X(k)H(k)Y(k)

Y(k)IFFTy(n)


10.8



  • 02


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