filter design fall11

8/13/2019 Filter Design Fall11

1/19

Digital Filter Design


2/19

(1) Frequency selective filters: spectral shapers

lowpass highpass bandpass bandstop

1. Introduction -- Digital Filter Design

FIR: - windowing

- equiripple design

IIR : - mapping from analog filters

- impulse invariance

(2)Filter Design Techniques

BGL/SNU


3/19

4. FIR Filter Design by Windowing

- Given a desired frequency response

evaluate

specification.giventheinfallspectrumfrequency

resultingthethatsuchor,segment offinite

Therefore, take apractical.notsolong,infinitelyis

However,coefficients.filterdesiredtheis- Then,

,)( jd eH

deeHnh njjdd )(

2

1][

This process of getting out of is

called Windowing

][nh ][nhd

(1) Design Concept

][nhd

][nhd

][nhd ][nh

,)( jeH


4/19

4

2. Window based method:

-30 -20 -10 0 10 20 30-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Ideal LPFc=/4

Shifting

-30 -20 -10 0 10 20 30-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Ideal LPFc=/4-shifted

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25LPF by Window Design Technique


5/19

5

Digital Filter Specifications

For example the magnitude response of a

digital lowpass filter may be given as indicated

below


6/19

Figure 7.2

magnitude response of

equivalent analog system

monotonous descent

2/1

c

passband

tolerance

c

stopband

tolerance

passband

cutoff

frequency

stopband

cutoff

frequency

3dB cutoff

frequency

absolute specification


7/19

7


In the passband we require that

with a deviation

In the stopband we require that

with a deviation

1)( jeG

0)( jeGs

pp0

s

pp

j

p eG

,1)(1

ssjeG ,)(


8/19

8


Filter specification parameters

- passband edge frequency

- stopband edge frequency - peak ripple valuein the passband

- peak ripple valuein the stopband

p

s

s

p


9/19

9


Practical specifications are often given in

terms of loss function (in dB)

Peak passband ripple

dB

Minimum stopband attenuationdB

)(log20)( 10

jeGG

)1(log20 10 pp

)(log20 10 ss


10/19

(3)Filter Specification(LPF)

|)(| jeH

11

1

11

2

0p

s

In some IIR filter design

11

1

1 2 3

1

2

3

ripplepassband:1

ripplepassband:2

],0[bandpassp

],[bandtransitionsp

],[bandstop s

BGL/SNU


11/19

1

decide specifications according to application2decide type according to specificationgenerally , if the phase is required ,

choose FIR.

3approach specifications using causal and stable discrete-time system

4choose a software or hardware realization structure, take effects of limited word

length into consideration

H(z) or h[n]

Design steps

Specifications for bandpass and bandstop filters

up and down passband cutoff frequency

up and down stopband cutoff frequency


12/19

otherwise

Mnnwnwnhnh d

,0

0,1][],[][][

)2

sin(

)

2

)1(sin(

11)(

)()(2

1)()()(

2/

)1(

0

)(

M

ee

eeeW

deWeH

eWeHeH

Mjj

MjM

n

njj

jj

d

jj

d

j

(2) Rectangular Windowing


13/19

0 2

1

2

M

sidelobepeak

lobemain

0 2

)( )( jeW)( j

d eH

)( jeH

)()(j

eW

j


14/19

n

n

n

)( jeW

)( jeH

)( jd eH

cc

1

2

M

0 M

][nhd

][nw

][nh

)(e

][][][ nhnwnh Rd )()()( jj

R

j

d eHeWeH


15/19

Window Design Techniques

Rectangular Window

otherwise,0

10,1)(

Mnnw

Exact transition width = s-

p= 1.8/M

Min. stopband attenuation = 21dB


16/19


Bartlett Window


p= 6.1/M


otherwise,0

12

1,

1

22

2

10,

1

2

)( MnM

M

n

Mn

M

n

nw


17/19


Hann Window


p= 6.2/M


otherwise,0

10)],1

2cos(1[50

)( MnM-

n

.nw


18/19


Hamming Window


p= 6.6/M


MATLAB function: w=hamming (M)

otherwise,0

10)],1

2cos(46.0540

)( MnM-

n

.nw

0 5 10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Hamming Window: M=45


19/19


Blackman Window


p= 11/M


otherwise,0

10)],1

4cos(08.0)

1

2cos(5.0420

)( Mn

M-

n

M-

n

.nw

0 5 10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Blackman Window: M=45

filter design fall11

Documents