9.lecture_lab_3

7/24/2019 9.lecture_lab_3

1/12

Lecture 9FIR and IIR Filter design using

Matlab

2007/11/16

Prof. C.M Kyung


2/12

FIR and IIR Filter

GOAL Linear-Time-Invarian !LTI" #y#em an$ Im%ue re#%on#e

'-Tran#form

C(ara)eri#i)# of *I+ an$ II+ ,&er#

e#ign %ro)e$ure of *I+ an$ II+ ,&er#


3/12

FIR and IIR Filter

LTI y#em In%u !!" or n" an$ Ou%u !y!" or yn" i# $e,ne$ ,r# *or a given #y#em i )an 3e ei(er LTI or non-LTI $e%en$ing on (o4

4e $e,ne (e in%u an$ ou%u.

Lineariy *or ar3irary an$ (e ou%u of (e #y#em for

i# (e #um (e ou%u for an$ . !#u%er%o#iion"

Time-invarian)e Time-#(if in in%u re#u in ime-#(if in ou%u 3y #ame amoun for

ime-invarian #y#em#.

][1 nx ][2 nx ][][][ 21 nxnxnx +=

][1 nx ][2 nx

]}[{][]}[{][ mnxoutputmnynxoutputny ==..ei

]}[{]}[{]}[][{ 2121 nxoutputnxoutputnxnxoutput +=+..ei


4/12

FIR and IIR Filter

Im%ue +e#%on#e e,niion Im%ue re#%on#e i# (e ou%u of (e #y#em 4(en im%ue #igna&

or i# a%%&ie$ a# (e in%u of (e #y#em.

Im%oran)e Im%ue re#%on#e 5fu&&y $e#)ri3e# (e #y#em if (e #y#em i# LTI.

8(y an$ (o49

8(y (e im%ue re#%on#e CA::OT fu&&y $e#)ri3e a non-LTI#y#em9

*ourier ran#form of (e im%ue re#%on#e #(o4# (e )(ara)eri#i) of(e #y#em i# fre;uen)y $omain.

)(t ][n


5/12

FIR and IIR Filter

'-Tran#form e,niion T(e '-ran#form of a #e;uen)e i# $e,ne$ a#


6/12

FIR and IIR Filter

I$ea& fre;uen)y-#e&e)ive ,&er A ,&er 4(o#e fre;uen)y re#%on#e i# uniy over a )erainfre;uen)y range an$ 'ero for o(er fre;uen)ie#.

*re;uen)y re#%on#e of an i$ea& &o4-%a## ,&er

>o4ever an i$ea& &o4-%a## ,&er i# non)au#a&.

-3 -2 -1 0 1 2 3-0.2

0

0.2

0.4

0.6

0.8

1

frequency

FrequencyResponse

Ideal Low pass filter


7/12

FIR and IIR Filter

*I+ / II+ ,&er e,niion If (e &eng( of (e im%ue re#%on#e i# ,nie (e ,&er i# an *I+ !,nie

im%ue re#%on#e" ,&er. O(er4i#e (e ,&er i# an II+ !in,nie im%uere#%on#e" ,&er.

*I+ In(eren&y ?I?O !3oun$e$-in%u 3oun$e$-ou%u" #a3&e :on'ero %o&e $oe# no ei# in i# ran#fer fun)ion


8/12

FIR and IIR Filter

*i&er e#ign Pro)e$ure e#ign )oninuou#-ime II+ ,&er O3ain $e#ire$ u#ing ?uer4or( C(e3y#(ev me(o$#

Conver i o $i#)ree-ime II+ ,&er u#ing im%ue invarian)e Im%ue invarian)e

if

O3ain $i#)ree-ime *I+ ,&er 3y 4in$o4ing (e II+ ,&er 8in$o4ing

Common&y u#e$ 4in$o4# re)angu&ar ?ar&e >anning >amming ?&a)Bman Kai#er

>o4ever 4in$o4ing $oe# no give (e o%imum #o&uion an$ o(era%%roa)(e# )an 3e u#e$.

)(sH

)(][ dcd nThTnh = )()(d

cj

TjHeH

=


9/12

FIR and IIR Filter

*re;uen)y re#%on#e of variou# ,&er#


10/12

FIR and IIR Filter

Pro3&em aemen# e#ign #evera& y%e# of *I+ an$ II+ ,&er#

II+ 3uer4or( )(e3y#(ev y%e1 )(e3y#(ev y%e 2

*I+ u#ing $iDeren 4in$o4# ! >amming >anning ?ar&e "

+emove (e noi#e in a)ou#i) #igna& u#ing (e ,&er# 8(a are (e $iDeren)e# 3e4een (e ,&er# 9

@n$er#an$ (e eDe) of #am%&ing fre;uen)y on (e#am%&e$ #igna& $i#orion !a&ia#ing"


11/12

FIR and IIR Filter


12/12

FIR and IIR Filter

+eferen)e#

*un$amena of igna& E y#em u#ing (e 4e3 an$

ma&a3 - e)B

i#)ree-Time igna& Pro)e##ing

- A&an F. O%%en(eim +ona&$ 8.)(afer

(%//444.ma(4orB#.)om/a))e##/(e&%$e#B/(e&%/oo&3o/#igna&/,&er$e.(m&
http://www.mathworks.com/access/helpdesk/help/toolbox/signal/filterde.htmlhttp://www.mathworks.com/access/helpdesk/help/toolbox/signal/filterde.htmlhttp://www.mathworks.com/access/helpdesk/help/toolbox/signal/filterde.htmlhttp://www.mathworks.com/access/helpdesk/help/toolbox/signal/filterde.html

9.lecture_lab_3

Documents

Transcript of 9.lecture_lab_3