dsp-第0章信号频谱分析

ysis

ofsignals

usingthe

DFTysis

of

sinusoidalsignalsfourierDFTthe

time-dependent

fourier

transformChapter

10

fourier ysis

of

signalsusing

discrete

fourier

transformFigure

10.110.1

fourierysis

of

signals

using

the

DFTFigure

10.2真实频谱滤波器非理想引入误差量化和混迭引入误差时域加窗和频域取样引入误差抗混迭滤波器频响窗序列频谱

2

/

N

/

T

2fs

/

Nf

/

2

fs

/

N10.2

DFTysis

of

sinusoidal

signals1.2.the

effect

ofwindowingthe

effect

of

spectral

samplingx[n]

A0

cos(0n

0

)

A1cos(1n

1)10.2.1

the

effect

ofwindowingX

(e

j

)

V

(e

j

)222211001100

)

)1

j1

j0

jj0j

)

e

(A

e

(AA

AX

(e

)

e

(

)

e

(

A0

e

j0

e

j0n

A0

e

j0

e

j0n

A1

e

j1e

j1n

A1

e

j1

e

j1n2

2

2

2Before

windowing:2

2V

(e

j

)

X

(e

j

)*W

(e

j

)

A0

e

j0W

(e

j(

0

)n

)

A0

e

j0W

(e

j(

0

)n

)2

2

A1

e

j1W

(e

j(

1)n

)

A1

e

j1W

(e

j(

1)n

)

A1

w[n]ej1e

j1n

A1w[n]e

j1e

j1n2

2After

windowing:v[n]

x[n]w[n]

A0

w[n]ej0

e

j0n

A0

w[n]e

j0

e

j0n2

2Figure

10.3(a)(b)Example

10.3EXAMPLE加窗前加窗后加窗的影响：谱线展宽成窗频谱的主瓣宽

产生旁瓣，衰减等于窗频谱的旁瓣衰减Figure

10.3(c)(d)(e)谱线展宽导致：

难以确定频率；降低频率分辨率产生旁瓣导致：产生假信号；淹没小信号谱example

10.8

:w[n]

(cos(

2

n)14

0.75

cos(

4

n))15kaiser

(L,5.48)Conclusion:

increase

L

can

increase

resolutionFigure

10.10EXAMPLEL

32L=32L=L42

42L=L54

54L=L64

64保守定义：频率分辨率=主瓣宽v[n]

(3.5

*

cos(

n)14

3.5

*

0.75

cos(

n))25wR

[n]

:

redwhanning

[n]

:

blueL

3222EXAMPLE改变窗形状能改变分辨率Conclusion:

shape

of

window

has

effect

on

frequency

resolutionslsl

13.26)A

13.2660

Asl

12013.26

Asl

60

.76609(

A

13.26)0

4

0.09834(

Asl0Determin

window’s

shape

and

length（2）for

blackman

window:look

up

the

table（1）

forkaiser

windows:

0.12438(

Asl

6.3)0L

24

(

Asl

12)

1

155mlml

:

main

lobe

widthAsl

:

relative

side

lobe

level10.2.2

theeffect

of

spectral

samplingV

(e

j

)

V[k]15L

6464

0.75

cos(

4

n))

R

[n]example

10

.4

:

w[n]

(cos(

2

n)14EXAMPLEAfter

samplingBefore

sampling峰值未取到N=64N=128864L

64

0.75

cos(

2

n))

R

[n]example10.5

:

v[n]

(cos(

2

n)16Figure

10.6EXAMPLEV[k]

X

(e

j

)

V

(e

j

)N=64只取到峰值和零值N=128Figure

10.7Conclusion

:

increase

N

canimprove

effectexample

10

.7

:w[n]

(cos(

2

n)14

0.75

cos(

4

n))15kaiser

(32,5.48)L

32Figure

10.9EXAMPLEConclusion:

increase

N

can’tincrease

resolutionN=32N=64N=128N=1024EXAMPLEs0

f

(t

)

|1

64

n

1280

n

63,T

1

/

ff

[n

]

f

2

[n

]

f

(t

)

|t

nT

0

n

128分别作128

点DFT

，比较二者的不同。t

nTf

(t

)

cos(

2f1t

)

cos(

2f

2t

),

f1

2

Hz

,

f1

2.5

Hz

,

f

s

64

Hz

,分析窗长对

DFT的影响L2=128;

N=128;

T=1/64x1=cos(2*pi*2*n1*T)+

cos(2*pi*2.5*n1*T)x2=cos(2*pi*2*n2*T)+

cos(2*pi*2.5*n2*T)L1=64;n1=0:L1-1;n2=0:L2-1;k=0:N-1;X1=fft(x1,N);stem(k,abs(X1));hold

on;X2=fft(x2,N)stem(k,abs(X2),’r.’);X

[n,

)

x[n

m]w[m]e

jmn

10.3

the

time-dependent

fourier

transform1.definition20

12X

[n,

)e

dx[n

m]w[n]

jmFigure

10.11Figure

10.12x[n]

cos(

0

n

2

)小结1.2.3.用DF