Bao Cao Tieu Luan-Binh

8/14/2019 Bao Cao Tieu Luan-Binh

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I HC NNG

TRNG I HC BCH KHOA

KHOA PFIEV

----

BO CO TIU LUN

GVHD : T.S NG VN S

SVTH : MAI V QUC BNH

Lp : 09CLC2

Nng, 2012

ti: Thit k b lc thng thp IIR, s dng

b lc ButterWorth v bin i song tuyn tnh


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MC LC

LI NI U ..................................................................................................... 1PHN I: BLC IIR V BI TON THIT K........................................ 2

I. Gii thiu chung vblc IIR:............................................................................ 21. Gii thiu: ...................................................................................................... 22. Hai cch tip cn: ........................................................................................... 2

II. Thit kblc IIR: ................................................................................................ 3III. Cc c im s b: ............................................................................................... 3

1. Tltuyn tnh tng i: .............................................................................. 32. Cc tnh cht ca |Ha(j)|2: ............................................................................ 4

PHN II: PHNG PHP THIT KBLC IIR................................... 5I. Cc c trng ca cc blc Analog in hnh:................................................. 5

1. Blc thng thp Butterworth: ...................................................................... 52. Blc thng thp Chebyshev: ....................................................................... 83. Blc thng thp Ellipic: ............................................................................ 114. Cc p ng pha ca cc blc in hnh: .................................................. 12

II. Cc php bin i blc tng tthnh blc s........................................... 121. Bin i bt bin xung: ................................................................................ 132. Bin i song tuyn tnh: ............................................................................. 15

III. Bin i bng tn: ................................................................................................ 17PHN III: CHNG TRNH THIT K.................................................... 20

I. Tnh ton thit k:............................................................................................... 20II. Thut ton gii quyt bi ton:.......................................................................... 22III. Chng trnh Matlab: ......................................................................................... 23

1. Cc hm sdng trong chng trnh: .......................................................... 232. Chng trnh: ............................................................................................... 263. Kt qu: ........................................................................................................ 284. M phng bng simulink: ............................................................................ 31

PHN IV: NH GI KT QU- KT LUN.......................................... 35I. Chtiu kthut: ................................................................................................. 35II. Cht lng lc thc t: ........................................................................................ 35

III. Kt lun: ............................................................................................................... 35


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Bo co tiu lun ------ Xl tn hiu s

Mai V Quc Bnh Lp 09CLC2 Trang 1

LI NI U

X l tn hiu s (Digital Signal Processing DSP) trthnh mt mn hc c s

cho nhiu ngnh khoa hc, kthut nh: in, in T, Tin hc, Vin thng, Tng ho ...X l tn hiu sc ng dng rng ri trong nhiu lnh vc v thit bnh: CD, VCD,DVD, camera, scanner, y khoa ..., trong cc hthng truyn hnh s, thng tin a l, bn s, vin thng ..v.v..

Php x l c bn nht ca DSP l lc, v cc h thng c cp n nhiu nhttrong xl tn hiu sl cc blc s(Digital Filter). Nu xt vp ng xung c thchiacc b lc s thnh 2 loi chnh l b lc c p ng xung hu hn FIR (Finite Impulse

Response) cn gi l lc khng quy, v blc c p ng xung v hn IIR (Infinte ImpulseResponse) cn gi l lc quy. Xt vp ng tn sbin c thchia cc blc, FIR

hay IIR, thnh 4 loi c bn: thng thp, thng cao, thng di v chn di. Cc blc ny cthc thit kbng nhng phng php khc nhau, mi phng php u c nhng uim v khuyt im ring.

Trong khun khca bi tiu lun mn hc ny, em xin php trnh by ni dung ti:

Bi ton thit kblc thng thp I I R, sdng blc Bu tterWorth vbin i songtuyn tnh.

Ni dung tiu lun c chia thnh 4 phn:

-Phn I: Blc IIR v bi ton thit k-Phn II: Phng php thit kblc IIR-Phn III: Chng trnh thit k-Phn IV: nh gi kt qu- kt lunEm xin trn trng cm n thy gio TS. Ng Vn S tn tnh hng dn, truyn t

nhng kin thc qu gi, cung cp ti liu tham kho v chbo cc phng php lm vickhoa hc.

Trong qu trnh lm tiu lun tuy ht sc cgng song chc chn khng trnh khi

nhng sai st. Rt mong nhn c sgp ca Thy ni dung ca tiu lun c honchnh hn.

Nng, ngy 21 thng 11 nm 2012Sinh vin thc hin

Mai V Quc Bnh


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PHN I:B LC IIR V BI TON THIT K

I. Gii thiu chung vblc IIR:1.Gii thiu:B lc IIR c p ng xung v hn, v vy chng c th khp vi cc b lc

analog, m ni chung u c p ng xung di v hn.

Kthut c bn thit klc IIR l bin i cc blc analogin hnh (well-known) thnh cc blc digitalsdng cc nh xgi tr-phc.

Sthun tinca kthut ny l chc sn cc bng thit klc analog (AFD)v cc nh xc mrng trong th vin.

Cc kthut c bn c gi l cc php bin i lc A/D.Tuy nhin, cc bng AFD ch dng cho cc b lc thng thp. Trong khi ta cn

thit kcc blc chn tn khc (thng cao, thng di, chn di, v.v)

Cn p dng cc php bin i bng tn i vi cc b lc thng thp. Cc phpbin i ny cng c gi l nh xgi tr-phc, v chng cng c sn trong thvin.

2.Hai cch tip cn:2.1. Cch 1, c sdng trong Matlab

2.2. Cch 2, c sdng hc tp, nghin cuDesign analoglowpass filter

Apply filtertransformation

s z

Apply freq. bandtransformation

z z

DesiredIIR filter

Design analoglowpass filter


s s


s z

DesiredIIR filter


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II.Thit kblc IIR:

Thit kblc thng thp analog. Nghin cu v p dng ccphp bin i blcthu c blc sthng thp. Nghin cu v p dng ccphp bin i bng tnthu c cc blc skhc

tblc sthng thp.

Cc vn tn ti :

Khng iu khin cc c tnh pha ca blc IIR. Cc thit klc IIR chxl nh cc thit kvbin .

III. Cc c im s b:1.Tltuyn tnh tng i: Ha(j)l p ng tn sca blc tng t. Cc c trng blc thng thp trn p ng bnh phng bin c cho bi:

2

2

2

2

1( ) 1,

11

0 ( ) ,

a p

a s

H j

H jA

Trong :

l thng sgn sngdi thng. Pl tn sct di thng (rad/s). A l tham ssuy hao di chn.

Sl tn sct ca di chn (rad/s).

Cc thng skthut ca blc thng tp Analog

Design analoglowpass filter


s z


z z

DesiredIIR filter

2

2

1( )

1

a PH j at

2

2

1( ) a SH j at

A


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Cc hthc gia , A, Rp, As, 1v210

10 2

2010 2

11

2

1 1

2 1

1 2

110log 10 1

1

1

10log 10

21 1

1 1 1

11

1

p

s

R

p

A

s

R

A AA

AA

2.Cc tnh cht ca |Ha(j)|2:Cc c trng ca blc Analog c cho theo cc hsca p ng bnh phng

ln, khng bao hm thng tin v pha. Do nh gi hm truyn h thng Ha(s) trongmin-s ta xt:

( ) ( )

a a s jH j H s

Sau ta c:2 *( ) ( ) ( ) ( ) ( ) ( ) ( )

a a a a a a a s jH j H j H j H j H j H s H s

Hay:2

/( ) ( ) ( )

a a a

s jH s H s H j

V vy cc im cc v im khng ca hm bnh phng bin c phn btheo

i xng nh-gng xt theo trc j.

i vi cc blc thc, cc im cc v im khng xut hin theo cp lin hp phc(hoc i xng nh-gng theo trc thc).

T cc mu ny chng ta c th xy dng Ha(s), l hm truyn h thng ca b lcanalog.

Ta mun Ha(s) biu din mt blc nhn quv n nh. Khi tt ccc im ccca Ha(s) trong na mt phng bn tri. Nh vy ta gn tt c cc im cc na-tri caHa(s)Ha(-s) ln Ha(s). Hoc chng ta schn cc im khng ca Ha(s)Ha(-s) nm bn cnh

hoc trn trc jnh cc im khng ca Ha(s).Blc kt quc gi l mt blc pha-ti thiu.


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PHN II:PHNG PHP THIT KB LC IIR

Nh ni phn trc, cc kthut thit klc IIR da trn blcAnalog c thu c cc blc s. Chng ta thit kcc blc Analog ny theo cc blc in hnh.

phn ny, ta stm hiu cc phn chnh sau:

1. Cc c trng vphng php thit kcc blc thng thp Analog in hnh.

2. Cc php bin i blc thu c blc sthng thp tblc Analog.

3. Cc php bin i bng tn thu c cc blc skhc tblc sthng thp.

I.

Cc c trng ca cc blc Analog in hnh:C ba kiu blc Analog in hnh c sdng rng ri trong thc t:

- Thng thp Butterworth.- Thng thp Chebyshev (Kiu I v II).- Thng thp Elliptic.

1.Blc thng thp Butterworth:1.1.

Cc c trng:

Blc ny c c trng bi tnh cht p ng bin l bng phngtrong cdithng v di chn.

p ng bnh phng-bin ca blc thng thp bc-N:2

2

1( )

1

a N

C

H j

Cl tn sct (rad/s)

thp ng bnh phng-bin :2

( )aH j


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Tthtrn ta c nhn xt: |Ha(0)|2=1 vi mi N. |Ha(jc)|2=0.5 vi mi N (hssuy gim 3dB c) |Ha(j)|

2

n iu gim theo Tin n blc l tng khi N

Xc nh hm truyn hthng Ha(s):2 2

2

2 22 2/

1

( ) ( )1( ) ( ) ( )

( )( )1

N N

C Ca a a N NN N

s jC

k

kC

j jH s H s H j

s js s pj

Cc im cc:1

2 2 (2 1)

( 1) ( ) , 0,1, ,2 1N Nj k N

k C Cp j e k N

Nhn xt vcc im cc ca ( ) ( )a aH s H s : C 2N im cc c phn bu n trn ng trn bn knh Cvi khong

cch gc / Nradians.

Vi N l, / , 0,1,..., 2 1jk Nk Cp e k N Vi N chn, 2 , 0,1,..., 2 1kj N Nk Cp e k N

i xng theo trc o. Mt im cc khng bao giri vo trc o, v ri vo trc thc chnuN l l. Mt blcn nh v nhn quHa(s) c thc xc nh bng cch chn cc

im cc trong na mt phng tri, v Ha(s) c thc vit di dng:

( )

( )

N

Ca N

k

LHP poles

H s

s p

Thi hnh trn Matlab:

Hm[z,p,k] = buttap(N) thit kmt blc Analog Butterworth chun ho (C = 1) bc N. z: zeros; p: poles; k: gain value.

Hm[b,a] = u_buttap(N,Omegac) thit kmt b lc Analog Butterworth cha chun ho vi C ty ,

bc N.

Cung cp mt cu trc dng trc tip vi: b l tthc, al mu thc. Hm[C,B,A] = sdir2cas(b,a) Chuyn i dng trc tip thnh dng ghp tng.


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1.2. Cc phng trnh thit k:Blc thng thp analog c c trng bi cc thng s , ,P P SR v SA . V vy u

im ca thit ktrong trng hp blc Butterworth l thu c bc N v tn sctC

.

Chng ta mun:

Ti 210, 10log ( )P a PH j R hay: 10 2110log1

PN

P

C

R

Ti 210, 10log ( )S a SH j A hay: 10 2110log1

SN

S

C

A

Gii 2 phng trnh trn ta thu c:

Bc

1010

10

10

log 10 1 10 1

2log

SP AR

P S

N

Tn sct C :- p ng thng skthut ti

P :

102 10 1PP

CRN

- p ng thng skthut tiS

: 102 10 1S

SC

AN

Thi hnh trn Matlab:

Hm[b,a] = afd_butt(Wp,Ws,Rp,As) thit kblc thng thp analog Butterworth, cho bi cc chtiu ca n.

Hm[db,mag,pha,w] = freqs_m(b,a,wmax) p ngbin tuyt i cng nh tng i theo thang dB v p ng pha.

Hm[ha,x,t] = impulse(b,a) p ng xung ha(t) ca blc Analog.

Phn tip theo sgii thiu thm vcc blc thng thp in hnh khc: Chebyshev,Ellipic, nhng do gii hn yu cu ca tiu lun ny nn skhng i su nh i vi blc

Butterworth.


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2.Blc thng thp Chebyshev:- Cc blc Chebyshev-I: C p ng cn bng gn sngtrong di thng.- Cc blc Chebyshev-II: C p ng cn bng gn sngtrong di chn- Cc blc Butterworth: C p ng n iutrong chai di.- Lu rng chn mt b lc cn bng gn sng thay v b lc n iu, ta thu

c mt blc c bc-thp.

V vy cc b lc Chebyshev cho bc thp hn so vi cc b lc Buttworth ccng chtiu.

2.1. Blc Chebyshev I: p ng bnh phng bin :

2

2 2

1( )

1

a

N

c

H j

T

Trong : N l bc blc

l hsgn sng di thng

a thc Chebyshev bc N

1

1

cos cos ( ) , 0 1( )cosh cosh ( ) , 1

N

C

N x xT x khi xx x

Vi 0 < x < 1, TN(x) dao ng gia1 v 1 Vi 1 < x < , TN(x) tng n iu n v cng

Hai dng thca p ng bnh phng-bin (N lvN chn)

Nhn xt:

Ti x = 0 (hoc = 0)2

2

2

( 0) 1 ( )1

( 0) ( )1

a

a

H j N odd

H j N even


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Ti x = 1 (hoc = C)2

2

1( 1) ( )

1aH j all N

Ti 0 x 1 (hoc 0 C), 2( )aH jx dao ng gia 1 v 211 Ti x > 1 (hoc > C), 2( )aH jx gim n iu v0. Ti x = r, 2 21( )aH jx A .Ha(s) nhn quv n nh:

xc nh mt hm Ha(s) nhn qu v n nh, ta phi tm cc im cc caHa(s)Ha(-s) v chn cc im cc na mt phng-trii vi Ha(s).

Cc im cc Ha(s)Ha(-s) thu c bng cch tm nghim ca:

2 21 NC

sT

j

C thchra rng nu , 0,1, , 1k k kp j k N l nghim (na mt phng tri)

ca a thc trn th:

(2 1)( )cos

2 2

(2 1)( )sin

2 2

k C

k C

ka

N

kb

N

0, , 1k N

Trong :

1 11/ , 1/2 2

N N N Na b

V2

1 11

Cc im cc ri trn mt ellipse vi trc chnh bcv trc phac.

Hm hthngl:

( )

a

k

KH s

s pk

Vi K l mt hschun ha c chn :

2

1,

( 0) 1 ,1

a

N odd

H j N even


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Thi hnh trn Matlab:

Hm[z,p,k] = cheb1ap(N,Rp) thit kmt b lc analog chun ho Chebyshev-I analog c bc N v

gn sng di thng Rp. z mng cc im khng p mng cc im cc trong p Gi trli k

Hm[b,a] = u_chb1ap(N,Rp,Omegac) Trli Ha(s) theo dng trc tip.

Cc phng trnh thit k:

Cho p, s, Rp v As, ba tham sc yu cu xc nh mt blc Chebyshev-I

Ta c:

/200.1

2 2

2

10

2

10

10 1 10

( 1) /

log 1

log 1

SP AR

SC P r

C

r r

and A

and

g A

g g

N

Thi hnh trn Matlab dng hm [b,a] = afd_chb1(Wp,Ws,Rp,As)

2.2. Blc Chebyshev II:Lin quan n blc Chebyshev-I thng qua mt php bin i n gin.

N c di thng n iu v di chn cn bng gn sng, ngha l blc ny c cccim cc v cc im khng trong mt phng-s.

V vy cc c trng trnhm l tt hn (v p ng pha tuyn tnh hn) trong dithng so vi blc Chebyshev-I prototype.

p ng bnh phng bin :

2

1

2 2

1( )

1

a

CN

H j

T

Thi hnh trn Matlab:

Function[z,p,k] = cheb2ap(N,As); Normalized Chebyshev-II


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Function[b,a] = u_chb2ap(N,As,Omegac) Unnormalized Chebyshev-II

Function[b,a] = afd_chb2(Wp,Ws,Rp,As)3.Blc thng thp Ellipic:

Cc blc ny thng cn bng gn sng di thng cng nh di chn. Chng c ccc trng p ng bin tng tnh cc blc FIR cn bng gn sng.

V vy cc blc elliptic l cc blc ti u trong t c bc ti thiu N i vicc chtiu cho

Cc blc ny, v nhiu l do xt trc y, l rt kh phn tch v thit k.

Khng ththit kchng bng cc cng cn gin, v thng phi dng cc chng

trnh hoc bng thit k.p ng bnh phng bin :

2

2 2

1( )

1

a

N

c

H j

U

N: bc : gn sng di thng UN() l hmJacobianelliptic bc-N

Hai dng thca p ng bnh phng-bin (N lvN chn)

Tnh ton cho blc bc N:

Vi

2

1 /2

12 2 202

1

( ) 1; , ; ( )

1 1 sin( ) 1

p

s

K k K k dN k k K x

A xK k K k


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Thi hnh trn Matlab:

Hm[z,p,k]=ellipap(N,Rp,As); Normalized elliptic analog prototype

Hm[b,a] = u_ellipap(N,Rp,As,Omegac) Unnormalized elliptic analog prototype

Hm[b,a] = afd_elip(Wp,Ws,Rp,As) Analog Lowpass Filter Design: Elliptic

4.Cc p ng pha ca cc blc in hnh: Blc Ellipticcho tnh nng ti u vp ng bnh phng-bin nhng c p

ng pha phi tuynhn trong di thng (khng thch hp cho nhiu ng dng). Ngay ckhi chng ta quyt nh khng lo lng g n p ng pha trong thit k,

pha vn givai tr quan trng trn ton hthng.

i vi cc blcButtworth , c p ng bin bng phng ti av i hi bcN cao hn (nhiu im cc hn) t c cng mt chtiu di chn. Tuy nhinchng c mt p ng pha khng tuyn tnh trong di thng.

Cc blc Chebyshev c cc c tnh pha nm gia. V vy trong cc ng dng thc t chng ta xem xtcc b lc Butterworth cng

nh Chebyshev, cng thm cc blc elliptic. Vic la chn phthuc vo cbc ca blc(thng nh hng n tc xl

v phc tp thi hnh) vcc c tnh pha(iu khin mo).

II.Cc php bin i blc tng tthnh blc s Sau khi kho st cc tip cn khc nhauthit kcc blc tng t, chng ta sn

sng bin i chng thnh blcs.

Cc php bin i ny t c bng cch bo toncc aspects khc nhau ca cc blc tng tv lc s.

- Bin i bt bin xung Bo ton hnh dang ca p ng xung tlc tng tthnh lc s

- Kthut xp xsai phn hu hn Chuyn i biu din mt phng trnh vi phn thnh mt phng trnh sai

phn tng ng.

- Bt bin bc nhy Bo ton hnh dng ca p ng bc nhy


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- Bin i song tuyn tnh Bo ton biu din hm hthng tmin tng tsang min s

Trong phn ny chcp n bin i bt bin xung v bin i song tuyn tnh.

1.Bin i bt bin xung:Trong phng php ny chng ta mun p ng xung ca blc strng tng tnh

p ng xung ca blc chn tn analog.

Ly mu ha(t) cc chu kly mu Tta thu c h(n):

ah n h nT

T c chn sao hnh dng ca ha(t) c gibi mu, lc ny:

j j T

T or e e

Do jz e trn ng trn n vv s j trn trc o, ta c php bin i sau y

tmt phng-s sang mt phng-z:

sTz e

Quan hgia hm hthngH(z) vHa(s) trong min tn s:

1 2( ) a

k

H z H s j kT T

nh xmt phng phc trong php bin i bt bin xung

Cc tnh cht:

= Re(s): < 0, nh xvo |z| < 1 (bn trong ng trn n v) = 0, nh xvo |z| = 1 (trn ng trn n v) > 0, nh xvo |z| > 1 (bn ngoi ng trn n v)

nh xnhiu s ln mt z : nh xmany-to-one


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2.Bin i song tuyn tnh:nh xny l phng php bin i tt nht.

1

1

2 1 1 / 2

1 1 / 2

z sT

s zT z sT

y T l mt tham s. Mt tn gi khc ca php bin i ny lBin i phn tuyn

tnh (linear fractional)v ta c: 1 02 2

T Tsz s z l tuyn tnh vi mi bin (s hoc z) nu

bin cn li c cnh, hoc song tuyn tnh vi s v z.

nh xmt phng phc trong php bin i song tuyn tnh

Cc nhn xt:

< 0, nh xvo |z| < 1 (bn trong ng trn n v) = 0, nh xvo |z| = 1 (trn ng trn n v)

> 0, nh xvo |z| > 1 (bn ngoi ng trn n v)

Ton bmt phng-na tri nh xvo bn trong vng trn n v. y l phpbin i n nh.

Trc o nh xln ng trn n vl nh x1-1. Do khng c aliasing trongmin tn s.

Quan hca theo lphi tuyn1 22 tan tan

2 2

T

T


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Thtc thit k:

Vi cc chtiu choca blc swp, ws, Rp, As, chng ta cn xc nh H(z). Ccbc nh sau:

1. Chn mt gi trTtu, v c tht T = 1.2. Chuyn i cc tn sct pv s, ngha l tnh ton p v s sdng:

,2 2

tan tan2 2

SPP S

T T

3. Thit kmt blc thng thp Ha(s) ph hp cc chtiu ny.

4. Cui cng ly:1

1

2 1( )

1a

zH z H

T z

. V nhn c H(z) l mt hm hu ttheo z-1

Thi hnh Matlab:Hm[b,a] = bilinear(c,d,Fs)

b = cc hstthc ca H(Z) a = cc hsmu thc ca H(Z) c = cc hstthc ca Ha(S) d = cc hsmu thc ca Ha(S) Fs = tn sly mu

Cc thun li ca bin i song tuyn tnh:

- L mt thit kn nh.- Khng baliasing (sai sly mu).- Khng rng buc vkiu blc c thbin i c.

So snh 3 blc:Chng ta thit kt blc ssdng 3 blc analog in hnh khc nhau (Butterworth,

Chebyshev, Ellipic). By gichng ta sso snh hiu quca chng. Thng skthut l:

wp = 0.2, Rp = 1dB, ws = 0.3, As = 15dB

Prototype Order N Stopband Att.

Butterworth 6 15

Chebyshev-I 4 25

Elliptic 3 27

R rng, blc Ellipic cho kt quthit ktt nht, bc N nhnht v min(As) l lnnht. Tuy nhin nu chng ta so snh p ng pha th thit ktheo Ellipic c p ng pha lphi tuyn nht trong di thng.


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III. Bin i bng tn:Mc ch ca phng php nyl thit kcc blc chn tn khc nhau:

- Cc blc thng cao- Cc blc thng di- Cc blc chn di

Bng cch sdng cc kt quca lc thng thp v php bin i bng tn.

Php bin i bng tn:

Gi HLP(Z) l b lc sprototype lowpass cho, v gi H(z) l b lc s chn tnc mong mun. Xc nh mt nh xtheo cng thc:

1 1( )Z G z

1 1( )such that ( ) ( ) |LP Z G zH z H Z

GisHLP(Z) l mt blc n nh v nhn qu, ta mun rng H(z) cng n nh vnhn qu. iu ny dn n cc yu cu sau:

1. G(.) phi l mt hm hu ttheo z-1sao cho H(z) l thi hnh c.

2. ng trn n v ca mt phng-Z phi nh x ln ng trn n v ca mtphng-z.

3. cho cc blc n nh, bn trong ng trn n vca mt phng-Z cng phi

nh xln bn trong ng trn n vca mt phng-z.

Cc thng skthut ca cc blc chn tn


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t v l bin tn sca Z v z, 'jZ e v jz e trn ng trn n vtngng ca chng. p ng 2 yu cu u tin, tc l:

1 1( ) ( ) 1jZ G z G e

V ' ( )( )jj j G ee G e e

Hay ' ( )jG e

Cng thc tng qut ca hm G(.) thomn cc yu cu trn l mt hm hu tcakiu ton-thng (all-pass type) c cho bi:

11 1

11

( ) , | | 11

nk

k

k k

zZ G z

z

(p ng yu cu 3)

Bng cch chn mt xp xbc n v cc hs ,k

chng ta c ththu c cc nhxkhc nhau. Cng thc c s dng rng ri nht cho cc php bin i ny c chotrong bng sau:

Bin i tn scho cc blc (blc thng thp nguyn mu c tn sct l c)


21/37



c kt li cc bc thit kblc schn tn:

1. Cc chtiu blc s-chn tn (LP, HP, BP, BS).

2. Chtiu blc sthng thp tnh tcc chtiu trn.

3. Chtiu blc Analog prototype.4. Tnh ton v thit kblc thng thp Analog prototype (4 kiu).

5. Dng cc php bin i chuyn thnh blc thng thp s.

6. Bin i bng tn blc sLP thnh blc s-chn tn mong mun.


22/37



PHN III:CHNG TRNH THIT K

Thit kda vo blc Butterworth v php bin i song tuyn tnh.

C hai hng th it k:

- Hng thnht:sdng trc tip cc thng skthut yu cu thit kblc s thng thp Analog Butterworth, sau bin i song tuyn tnh thuc blc sthng thp.

- Hng th2:Sdng mt blc sthng thp thit ktrc (dng blcButterworth v bin i song tuyn tnh), sau thc hin php chuyn i bng

tn thu c blc thng thp sc thng skthut theo yu cu.Di y sthit ktheo hng thnht, cn hng thhai thc hin tng t, sau

sdng cng thc trong phn Php bin i bng tn (cui Phn II) chuyn i Lowpasssang Lowpass.

I. Tnh ton thit k:Cho blc thng thp c thng snh sau:

0.3 , 0.4 , 50 , 0.5p s As dB Rp dB

- Chn chu kly mu T = 1- Chuyn i ,p s (tnh ton ,p s )

2 2 0.3tan tan 1.019 ( / )

2 1 2

2 2 0.4tan tan 1.453 ( / )

2 1 2

p

p

ss

rad sT

rad sT

- Thit kblcHa(s) tha mn chtiu ny:Tnh bc blc v tn sct:

1010 0.5 10 50 10

10 10

10 10

log 10 1 10 1 log 10 1 10 120

2log 2log 1.019 1.453

SP AR

P S

N

0.5 1010 2*2021.019

1.074 ( / )10 110 1P

PC

RN

rad s

Hoc:

50 1010

2*202

1.4531.0896 ( / )

10 110 1S

SC

A

N

rad s

Ta c thchn C gia 2 gi trtrn, chn 1.08 ( / )C rad s


23/37



Suy ra p ng bnh phng bin :

2

2 2 2040

40

1 1 1( )

1111 1.081.08

a N

c

H j

2

/

40 40

40 40

( ) ( ) ( )

1 1

1 11 ( / ) 1

1.08 1.08

a a as j

H s H s H j

s j s

20

11 12 29 30

1.08( ) ( )

( )( )...( )( )a aH j H s

s s s s s s s s

Trong 11 12 29 30, ... ,s s s s l nghim ca mu thc ( ) ( )a aH s H s na mt phng bn tri.

Xc nh H(z):1 1

1 1

1

2 1 1( ) 2

1 1a a

T

z zH z H H

T z z

Nh vy ta nhn c H(z) l mt hm hu ttheo z-1.

Phn tip theo sgii thiu vthut ton v chng trnh thc hin.

S1

S10

S20

S30

S40


24/37



II.Thut ton gii quyt bi ton

MRNG

a tn hiu vo xvi

2

Smax

Ff

Filter(va thit k)

Phn tch phtn hiu xvydng bin i FFT

Vth:- Tn hiu vo theo thi gian- Tn hiu ra theo thi gian- Phtn hiu vo- Phtn hiu ra

Tn hiu u ra y

Begin

Nhp cc chtiup, s, As, Rp

Fs = 1000; T = 1/Fs

2tan

2

2 tan2

p

P

sS

T

T

Tnh Ha(s)

[ , ] _ ( , , , )P S P Scs ds afd butt R A

Bin i song tuyn tnh thu c H(z)

- Dng trc tip: [ , ] ( , , )S

b a bilinear cs ds F

- Dng ghp tng: [ , , ] 2 ( , )C B A dir cas b a

Tnh p ng bin [ , , , , ] _ ( , )db mag pha grd w freqz m b a

Tnh gi trAs

v Rpthc t

- V mt phng nghimphc s-plane v z-plane.- V p ng bin ,

pha ca blc thit k.- Vha(t) v h(n)

END


25/37



III. Chng trnh Matlab:1.Cc hm sdng trong chng trnh:

Hm[cs,ds] = afd_butt(OmegaP,OmegaS,Rp,As)

thit kblc thng thp analog Butterworth, cho bi cc chtiu ca n.

Hm[b,a] = u_buttap(N,Omegac) (sdng bn trong hm afd_butt)

thit kmt blc Analog Butterworth cha chun ho vi C ty , bc N.

function[b,a] = u_buttap(N,Omegac);% Unnormalized Butterworth Analog Lowpass Filter Prototype% --------------------------------------------------------% [b,a] = u_buttap(N,Omegac);% b = numerator polynomial coefficients of Ha(s)% a = denominator polynomial coefficients of Ha(s)% N = Order of the Butterworth Filter% Omegac = Cutoff frequency in radians/sec%[z,p,k] = buttap(N);p = p*Omegac;k = k*Omegac^N;B = real(poly(z));b0 = k;b = k*B;a = real(poly(p));

function[b,a] = afd_butt(Wp,Ws,Rp,As);% Analog Lowpass Filter Design: Butterworth% -----------------------------------------% [b,a] = afd_butt(Wp,Ws,Rp,As);% b = Numerator coefficients of Ha(s)% a = Denominator coefficients of Ha(s)% Wp = Passband edge frequency in rad/sec; Wp > 0% Ws = Stopband edge frequency in rad/sec; Ws > Wp > 0

% Rp = Passband ripple in +dB; (Rp > 0)% As = Stopband attenuation in +dB; (As > 0)%ifWp


26/37



Hm[b,a] = bilinear(cs,ds,Fs)

Bin i song tuyn tnh chuyn Ha(s) thnh H(z)

b = cc hstthc ca H(z)

a = cc hsmu thc ca H(z)cs = cc hstthc ca Ha(s)

ds = cc hsmu thc ca Ha(s)

Fs = tn sly mu

Hm[db,mag,pha,grd,w] = freqz_m(b,a);

Tnhbin tng i (dB), bin tuyt i, pha, nhm tr, di mu tn sthm hthng H(z) c hstthc l b, hsmu thc l a .

Hm[C,B,A] = dir2cas(b,a): Chuyn i dng trc tip thnh dng ghp tng.

function[b0,B,A] = dir2cas(b,a);

%DIRECT-form to CASCADE-form conversion (cplxpair version)%......................................................... %[b0,B,A]=dir2cas(b,a)%b0=gain coefficient%B= K by 3 matrix of real coefficient%A= K by 3 matrix of real coefficient%b = numerator polynomial coefficient of DIRECT form%a = numerator polynomial coefficient of DIRECT form% compute gain coefficient b0b0 = b(1); b = b/b0;a0 = a(1); a = a/a0;

b0 = b0/a0;

function [db,mag,pha,grd,w]=freqz_m(b,a);% Modified version of freqz subroutine%.................................. % [db,mag,pha,grd,w]=freqz_m(b,a);% db=Relative magnitude in dB computed over 0 to pi radians% mag=absolute magnitude computed over 0 to pi radians% grd= Group delay over 0 to pi radians% w=501 frequency samples between 0 to pi radians% b=numerator polynomial of H(z) (for FIR: a=h)% a=demonitor polynomial of H(z) (for FIR: a=[1])%[H,w]=freqz(b,a,1000,'whole');H=(H(1:1:501))';w=(w(1:1:501))';mag=abs(H);db=20*log10((mag+eps)/max(mag));pha=angle(H);grd=grpdelay(b,a,w);


27/37



Mt shm khc:

Hm [bz,az] = zmapping(bZ,aZ,Nz,Dz): Chuyn i bng tn thu c ccblc chn tn khc tblc thng thp sthit kc.

Hm [ha,x,t] = impulse(cs,ds): p ng xung ha(t) ca blc Analog Hm y = filter(b,a,x) Lc tn hiuxqua hthng H(z) c hstthc l b, hsmu thc l a. y l tn hiu thu c sau khi lc

Hm fft(x,n) Bin i Fourier nhanh tn hiu x vi n im. y ng dng phn tch phtn hiu vo ra.

Hm zplane(num,den): vim zeros v im poles trn mt phng phc Hm freqz(b,a): vp ng bin (dB) v p ng pha ()

M = length(b);N = length(a);

ifN > Mb=[b zeros(1,N-M)];

elseifM > N

a=[a zeros(1,M-N)];N=M;else

NM=0;end

%K=floor(N/2);B = zeros(K,3);A = zeros(K,3);

ifK*2 == N;b=[b 0];a=[a 0];

end

%broots = cplxpair(roots(b));aroots = cplxpair(roots(a));fori=1:2:2*K

Brow = broots(i:1:i+1,:);Brow = real(poly(Brow));

B(fix((i+1)/2),:) = Brow;Arow = aroots(i:1:i+1,:);Arow = real(poly(Arow));

A(fix((i+1)/2),:) = Arow;end


28/37



2.Chng trnh:clear all

close all

clc

% Nhp cc thng skthut

wp = input(' - Tan so cat canh dai thong wp = ');

ws = input(' - Tan so cat canh dai chan ws = ');

As = input(' - Suy hao dai chan As = ');

Rp = input(' - Do gon song dai thong Rp = ');

%% Thit kthng thp

%%

Fs = 1000;

T = 1/Fs;

f_pass = wp*Fs/2/pi;

f_stop = ws*Fs/2/pi;

fprintf('\nDai chuyen tiep: [%5.1f,%5.1f]Hz\n',f_pass,f_stop);

OmegaP = (2/T)*tan(wp/2);

OmegaS = (2/T)*tan(ws/2);

[cs,ds] = afd_butt(OmegaP,OmegaS,Rp,As);

%% Bin i song tuyn tnh

%%

[b,a] = bilinear(cs,ds,Fs);

[db,mag,pha,grd,w]=freqz_m(b,a);[C,B,A] = dir2cas(b,a)

delta_w=pi/500;

Asd = floor(-max(db(ws/delta_w+1:500)))

Rpd = -min(db(1:wp/delta_w+1))

%% Dap ung xung

[ha,x,t] = impulse(cs,ds);

[delta,n] = impseq(0,0,50);

h=filter(b,a,delta);

%% Cc tn hiu vo%%

nth = 0:1/Fs:2;

f1=150; f2=200; f3=280; f4=350;

TH1 = 2*sin(2*pi*f1*nth);

TH2 = 2*cos(2*pi*f2*nth);

TH3 = 2*sin(2*pi*f3*nth);

TH4 = 2*cos(2*pi*f4*nth);

TH = TH1+TH2+TH3+TH4;

%% Lc tn hiu

y = filter(b,a,TH); % y l tn hiu ra


29/37



%% Phn tch phtn hiu

spec_in=abs(fft(TH,512)); spec_in = spec_in(1:257); % chly 1 na

spec_out=abs(fft(y,512)); spec_out = spec_out(1:257);

f = Fs*[0:256]/512;

%% Mat phang nghiem phuc

figure(1)

subplot(2,1,1); zplane(cs,ds); title('s-plane','fontsize',12);

subplot(2,1,2); zplane(b,a); title('z-plane','fontsize',12);

%% Vp ng bin

figure(2);

subplot(2,2,1);

plot(w/pi,mag,'Linewidth',2);grid

title('Magnitude Response','fontsize',12);

ylabel('|H|'); xlabel('w/pi');

axis([0 1 -0.1 1.1]);

set(gca,'XTickMode','manual','XTick',[0;wp/pi;ws/pi;1]);

set(gca,'YTickMode','manual','YTick',[0;1]);

subplot(2,2,2);

plot(w/pi,db,'Linewidth',2);grid ;

title('Magnitude in dB','fontsize',12);

ylabel('Decibels'); xlabel('w/pi');

axis([0 1 -Asd-3 2]);

set(gca,'XTickMode','manual','XTick',[0;wp/pi;ws/pi;1]);set(gca,'YTickMode','manual','YTick',[-Asd;0]);

subplot(2,2,3);

plot(t,ha);grid;

title('Impulse Response Analog','fontsize',12);

axis([0 50*T floor(min(ha))-50 ceil(max(ha))+50]);

subplot(2,2,4)

stem(n,h);grid

title('Impulse Response Digital','fontsize',12);

axis([0 50*T -0.5 0.5]);figure(3)

freqz(b,a); %Ve dap ung bien do va dap ung pha trn 1 ca s

%% Vtn hiu u vo, u ra

figure(3)

Sam = 100;

subplot(2,2,1)

plot(nth(1:Sam),TH(1:Sam));

title('Input Signal','fontsize',12);

axis([0 nth(Sam) min(TH)-0.5 max(TH)+0.5]);subplot(2,2,2)

plot(nth(1:Sam),y(1:Sam));


30/37



title('Output Signal','fontsize',12);

axis([0 nth(Sam) min(TH)-0.5 max(TH)+0.5]);

% Vphtn hiu

subplot(2,2,3)

plot(f,spec_in);%grid

title('Spectrum of the Input Signal','fontsize',12);

xlabel('Frequency (Hz)');

ylabel('Magnitude');

axis([0 Fs/2 -1 max(spec_in)+2]);

set(gca,'XTickMode','manual','XTick',[0;f1;f2;f3;f4;Fs/2]);

subplot(2,2,4)

plot(f,spec_out);%grid

title('Spectrum of the Output Signal','fontsize',12);

xlabel('Frequency (Hz)');

ylabel('Magnitude');

axis([0 Fs/2 -1 max(spec_in)+2]);

set(gca,'XTickMode','manual','XTick',[0;f1;f2;f3;f4;Fs/2]);

3.Kt qu:- Tan so cat canh dai thong wp = 0.5*pi

- Tan so cat canh dai chan ws = 0.6*pi

- Suy hao dai chan As = 50

- Do gon song dai thong Rp = 0.5

Do rong dai tan chuyen tiep: [250.0, 300.0]Hz

*** Butterworth Filter Order = 22

C =

4.4762e-006

B =

1.0000 3.3221 2.7806

1.0000 3.0243 2.4289

1.0000 2.6183 1.9509

1.0000 2.2487 1.5214

1.0000 1.9405 1.1696

1.0000 1.7669 0.8096

1.0000 1.6944 0.8903

1.0000 1.5088 0.6817

1.0000 1.3707 0.5307

1.0000 1.2765 0.4303

1.0000 1.2289 0.3802


31/37



A =

1.0000 0.0892 0.8670

1.0000 0.0788 0.6497

1.0000 0.0708 0.4825

1.0000 0.0646 0.35251.0000 0.0598 0.2511

1.0000 0.0560 0.1721

1.0000 0.0531 0.1113

1.0000 0.0509 0.0657

1.0000 0.0494 0.0331

1.0000 0.0484 0.0121

1.0000 0.0479 0.0018

As thuc te:

Asd =

51

Rp thuc te:

Rpd =

0.3844


32/37




33/37



Ta tnh c tn sct ca blc ny l fc= 256.9Hz 2c

c Sf F

Quan st phca tn hiu, ta thy u vo thp gm 4 thnh phn c tn sln lt l150Hz, 200Hz, 280Hz, 350Hz.

Blc thng thp ny c tn sct fc= 256.9Hz nn chcho tn hiu c tn s150Hzv 200Hz i qua, hai tn hiu cn li bchn, ta c thddng thy iu ny qua phca tnhiu u ra.

4.M phng bng simulink:ca scommand, gsimulink, to mt file mi v thit ks nh hnh di y


34/37



Cc khi trong s trn:

- Khi Lowpass filter (FDATool):Ta dng khi ny thit kblc IIR Butterworth c cc thng s

wp = 0.5*pi, ws = 0.6*pi, As = 60dB, Rp = 0.5dB

- Cc khi tn hiu: Tn hiu 1: Tn hiu sin ri rc c tn s350Hz, Fs = 1000sam/s Tn hiu 2: Tn hiu sin ri rc c tn s150Hz, Fs = 1000sam/s Tn hiu 3: Tn hiu ri rc c tn sbin thin lin tc trong khong 50Hz n

400Hz, Fs = 1000sam/s.

- Cho 3 tn hiu vo bcng lm tn hiu u vo ca blc IIR- Hai khi phn tch tn hiu u vo v u ra

Chy m phng ta thu c kt qunh sau:


35/37



Tn hiu u vo

Hnh trn gm c 3 th:- Tn hiu vo theo thi gian (s)- Mt cng sut phbin Mag2/(rad/s), do tn hiu vo gm c 3 thnh phn vi 3

tn skhc nhau, nhn vo thta thy r rng mt cng sut phca 3 tn hiu nyng vi 3 gi trtn s(y theo n vrad/s).

350Hz 2199rad/s

150Hz 942.5rad/s

Tn hiu cn li c tn sbin thin theo thi gian

- Mt phpha


36/37



Tn hiu u ra

Theo tnh ton th blc ny c tn sct l fc= 256.9Hz do n chcho tn hiu ctn s150Hz qua, hai tn hiu kia bchn li

Nhn vo thta thy r rng chcn li phca tn hiu c tn s150Hz, v dng tnhiu trong min thi gian l dng sin.


37/37


PHN IV:NH GI KT QU - KT LUN

I. Chtiu kthut: p ng c cc thng skthut nh yu cu ( , , , )P S S PA R p ng bin bng phng ti av i hi bc N cao hn(nhiu im cc hn)

t c cng mt chtiu di chn. Tuy nhin chng c mt p ng pha khngtuyn tnhtrong di thng (nhn vo p ng pha vc, ta thy pha gn tuyn tnh).

Nhp dng phng php bin i song tuyn tnh (phng php bin i tt nht)nn blc sthu c:- p ng tt cc chtiu kthut.- Khng c aliasing (sai sly mu) trong min tn s.- Blc thit kl n nh (cc im cc u nm trong ng trn n vz-plane)- Tuy nhin quan hgia theo lphi tuyn.

II.Cht lng lc thc t: Quan st qu trnh m phng vi tn hiu vo trn, ta nhn thy blc thit khot

ng tng i tt.

Nhp ng bin bng phng trong chai di nn hu nh khng gy mo m tnhiu i qua di thng cng nh lm suy gim hon ton (theo chtiu) tn hiu qua dichn

Tuy nhin chng ta vn quan st thy tn hiu ra btrpha so vi tn hiu voIII. Kt lun:

Tiu lun tm tt cc vn l thuyt c bn vthit kblc sIIR. Nu cc c

tnh b lc s cn xc nh v cc phng php khi thit k b lc: S dng 4 kiuButterworth, Chebyshev 1-2, Ellipic. Tiu lun i su nghin cu phng php thit kblc IIR thng thp sdng blc Butterworth v php bin i song tuyn tnh.

Sau khi tm hiu l thuyt c bn ca phng php ny, tiu lun vn dngMATLAB minh ha l thuyt ng thi nu ra bi ton thit kv cch gii quyt, so snhkt qut c.

Tuy ht sc cgng nhng chc chn tiu lun vn cn nhiu thiu st, rt mongnhn c sgp ca Thy ni dung ca tiu lun c hon chnh hn.

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