MC LCLI M U3CHNG I: TM HIU V HM FFT TRONG MATLAB4( Fast Fourier Transform)41.1.Bin i Fourier41.2.Hm FFT trong Matlab51.2.1.nh ngha, chc nng hm51.2.2. Cu trc hm v v d5CHNG II: TM HIU V B LC NOTCH FILTER82.1. Tm hiu chung82.2. nh hng cc thng s ti b lc9CHNG III: PHNG PHP X L S LIU113.1.Phng php x l s liu113.1.1.M phng tn hiu113.1.2.Tnh ton ng bao bin 12CHNG IV: THAO TC PHN TCH TN HIU C TH14CHNG V:THC HNH155.1.S dng FFT tm cc tn s chnh ca tn hiu155.2.Dng Notch Filter tch tn hiu.175.2.1.Tch ly tn hiu tn s 15Hz175.2.2.Tch ly tn hiutn s 10Hz.215.3.So snh kt qu255.3.1.Tn hiu tn s 10Hz255.3.2.Tn hiu tn s 15Hz265.4.Thit k b lc bng Matlab27Kt lun chung29Ti liu tham kho30

LI M U Ngy nay,cc h thng iu khin t ng ang chim mt vai tr quan trng trong vic pht trin v tin b ca vn minh hin i v khoa hc k thut. T yu cu v truyn pht cc tn hiu s phc v vic iu khin v gim st cng tng cao. tng hiu sut s dng cc h thng, cc tn hiu s truyn i thng l tng hp tn hiu ca nhiu thit b. Ngoi ra, trong qu trnh truyn dn tn hiu s b nh hng bi nhiu t mi trng. Chnh v vy cn thit k cc b lc s phn tch tn hiu mt cch chnh xc bn thu c th phn tch, nh gi v gim st h thng.Trong n ny,em s trnh by v vic nhn dng m hnh ton hc bc 2,phn tch v xy dng phng trnh ng bao cho cc tn hiu thnh phn t mt tn hiu tng cho trc. thc hin n ny em xin chn thnh cm n TS.Dng Minh c tn tnh hng dn, gip em c nhng kin thc cn bn v x l tn hiu v lc s.Vi thi gian v kin thc cn hn ch nn n ca em khng trnh khi nhng sai st. Em mong thy s c nhng gp b sung n ca em c hon thin hn.

Em xin chn thnh cm n!Sinh vin thc hin

CHNG I: TM HIU V HM FFT TRONG MATLAB( Fast Fourier Transform)

1.1. Bin i Fourier

Tn hiu thc t thng bao gm cc thnh phn c tn s khc nhau. Chui Fourier v php bin i Fourier l cng cc ton hc dung phn tch c tnh tn s ca tn hiu. C 4 nh ngha v chui v php bin i Fourier gm: Chui Fourier lin lc theo t(CFS), php bin i Fourier lin tc theo t (CFT), chui Fourier gin on theo t(CFS) v php bin i Fourier gin on theo t(DFT).

Ta c phng trnh bin i Fourier lin tc nh sau:

Tuy nhin tn hiu ta thu c thng l tn hiu ti cc thi im gin on. c th x l c ta cn php bin i Fourier gin on (DFT) tnh xp x cng thc , ta thay php tch phn bi php tnh tng N din tch nh ch nht c chiu cao l vi l chiu rng ca cc hnh ch nht( chu k trch mu ca php o c c bng cch ly mu mt tn hiu lin tc h(t) T ln trong mt giy), l tn s trch mu v l s lng gi tr o.

Ni chung h s DFT ca l mt s phc v n xc nh bin v pha ca thnh phn tn hiu c tn s tng ng vi tn s tng t . phn gii tn s l ( tn s c bn s) hoc ( tn s c bn tng t) l t l nghch vi khong thi gian o,l hiu tn s c th phn bit bi N im DFT. Tn hiu v DFT ca n ko di hu hn trn phm vi thi gian/ tn s

1.2. Hm FFT trong Matlab

1.2.1. nh ngha, chc nng hm

Bin i Fourier nhanh FFT l thut ton hiu qu tnh DFT c xy dng bng cch dung tnh chu k v tnh i xng ca nhn t gim bt s nhn t phc t thnh , N th hin kch thc ca DFT. Thut ton FFT phn tch theo thi gian phn tch dy thnh cc dy con nh hn.Lnh fft(x) ca MATLAB c tc dng to vector s liu tr li kt qu di dng mt vector c cng di vi , v cc h s Fourier. Cc h s Fourier c hai khong i xng v .Nu cn xc nh cc h s thc ca chui Fourier:

Bng cng c DFT, ta cn ch ti chu k trch mu T v chun ha kt qu bng thi gian o NT. lm iu v xt ti chiu rng T ca lng t din tch hnh ch nht, ta chia cc phn t ca cho N. ng thi ta tch di tn trn ra v gp i s phn t cn li ( khng k thnh phn mt chiu c ch s 1).

1.2.2. Cu trc hm v v d

Cu trc hm:Trong Matlab thut ton Fast Fourier Transform c cu lnh l . Trong x l chui d liu x[n].

V d:Trong v d di y, trc ht ra to ra mt vector gi tr o km theo vector thi gian . Sau xc nh chu k trch mu , s lng ca php o (v vector tn s . Kt qu bin i c chun ha v hn ch vo phm vi. Tn hiu o v ph tn c minh ha bi th.

t = 0.01 : 0.001 : 0.5 ;x = 5 + 8*sin(2*pi*8*t) + 4*cos(2*pi*33*t); T = diff (t(1:2));N = length(x);f = [0:(N-1) / 2] / (N*T);H = fft(x);H= H/N;H = [H(1) 2*H(2:N/2)];figure;subplot(121);plot(t,x);title('Signal' , ' FontSize ' ,12);subplot(122);plot(f,abs(H),'o');xlabel('Frequency [Hz] ', 'FontSize',12);title('Spectrum', 'FontSize',12);

Hnh 1: p ng tn s v bin ca tn hiu

Trong v d trn, chu k trch mu v tn s cao nht c th o c l . C tt c 50 gi tr o c x l. phn gii tn s l . Ph c tnh cho cc tn s , nu xut hin mt thnh phn tn s ca tn hiu o c nm gia cc tn s tnh ( nm gia cc chm trn) l do hin tng d tn s gy nn : bin c phn b ri sang c cc tn s ln cn. Hin tng ny s xut hin khi khong thi gian o khng phi l bi s ( gp mt s nguyn ln) ca chu k ca thnh phn tn hiu cn c phn tch.

Vic chn phn gii tn s mn hn nhm mc ch loi tr d tn s cng ch c tc dng hn ch, v qua tp m s c nh hng mnh hn. Hiu php tt hn l s dng cc hm ca s hoc to ra cc gi tr trung bnh.

CHNG II: TM HIU V B LC NOTCH FILTER2.1. Tm hiu chungMch lc l mt lp c bit ca cc h thng tuyn tnh bt bin vi thi gian. Mch lc- chn lc tn s l mt h thng ch cho qua cc thnh phn tn s nht nh v ct b ton b cc thnh phn tn s khc. Da trn p ng tn s ca hm truyn, mch lc c phn thnh 4 loi c bn: Thng thp ( Low- Pass Filter:LPF), thng cao(High- Pass Filter:HPF), thng di (Bandpass Filter :BPF) v chn di (Bandstop Filter:BSF).Notch Filter l mt loi mch lc tn s c 3 trng hp p ng tn s nh sau:

Trong ti liu ny ta tm hiu trng hp b lc tn s Notch Filter c dng chun Standard Notch.Vi trng hp ny, hm truyn ca b lc Notch s c dng:

2.2. nh hng cc thng s ti b lc

Ta c hm truyn ca b lc:

Trong l tn s ct ca b lc(hng s) nh vy ta ch xt s nh hng ca 2 thng s l v ti b lc.

Xt

GG1G2G3G4

0.030.020.040.04

0.010.010.050.06

Thc hin lnh trong Matlab:

G1=tf([1 0.3 25],[1 1 25]);

bode(G1,'-'), grid

hold on

G2=tf([1 0.2 25],[1 1 25]);

bode(G2,'--'), grid

G3=tf([1 0.4 25],[1 0.5 25]);

bode(G3,':'), grid

G4=tf([1 0.4 25],[1 0.6 25]);

bode(G4,'-.'), grid

Ta thu c th sau:

Nh ta thy, vi hm truyn G1 v G2 th di tn s ct ca G2 nh hn G1( tc lc chnh xc hn). Cn vi hm truyn G3 v G4 th th di tn s ct ca G4 nh hn G3. Hay ta c th kt lun rng vi t s / cng nh th cht lng ca b lc Notch Filter cng tt.

CHNG III: PHNG PHP X L S LIU

3.1. Phng php x l s liu

Hm truyn tn hiu c dng:G(s)= ta cn xc nh thng s ca tn hiu.

Bc tin hnh:Bc 1: M phng hm truyn vi kch thch u vo Impulse.Bc 2: Tnh ton phng trnh ng bao bin ca tn hiu thu c.Bc 3: Qua cng thc ng bao l thuyt xc nh thng s .3.1.1.M phng tn hiuHm truyn tn hiu c dng:G(s)=

Vi p ng u vo l tn hiu Impulse, ta thu c dng tn hiu u ra .

Nh ta thy, th tn hiu thu c c dng tt dn.Phng trnh ng bao bin :

3.1.2.Tnh ton ng bao bin

Ta s dng phng php bnh phng cc tiu tnh ton phng trnh ng bao bin .

Phng php bnh phng cc tiu:Gi thit c hm thc nghim:

Trong n l s im cc i. n gin ta thay hm thc nghim bng a thc gn ng:

Tin hnh tnh cc h s a v b ngha l vi cc gi tr ny, th ca a thc s i gn st vi cc im trong . K hiu l lch ca gi tr so vi gi tr bng v khi t vo phng trnh (1) ln lt tng cp gi tr bng , ta vit c phng trnh lch:

Trong h phng trnh ny ta coi cc s a, b l cc s cha bit cn cc gi tr l cc h s cho.

Nh vy gi tr tt nht ca cc s a, b c c khi tng bnh phng lch l nh nht, ngha l:

Hoc = cho hm f(a,b) c gi tr nh nht, cc o hm ring theo a v b phi trit tiu, ngha l:

Ly o hm ting ca phng trnh (*), ta nhn c h phng trnh i vi cc h s a,b cha bit:

H phng trnh c th gii c bng phng php i s t ta xc nh c h s a v b.

CHNG IV: THAO TC PHN TCH TN HIU C THTa c tn hiu cn phn tch dng:

Trong : v l 2 tn hiu chnh v l 1 tn hiu nhiu.

Trnh t thc hin:

Bc 1: S dng FFT xc nh 2 tn s v .Bc 2: S dng NotchFilter tch ln lt tng tn hiu ra khi tn hiu tng.Bc 3: Xc nh cc im cc i ca tng tn hiu n l.Bc 4: S dng phng php bnh phng cc tiu vit phng trnh ng thng i qua cc im cc i ca tn hiu. T suy ra dng phng trnh tn hiu.

CHNG V:THC HNHTa gi thit tn hiu dng kho st l tng 2 tn hiu c tn s 10Hz v 15Hz, ngoi ra c thm tn hiu nhiu:y= 20.sin(2.10t) + 35.sin(2.15t). +u(t)Trong : 20.sin(2.10t) v 35.sin(2.15t). l 2 tn hiu chnh v u(t) l 1 tn hiu nhiu.5.1. S dng FFT tm cc tn s chnh ca tn hiut=0:0.0001:1;k1=2*pi*10;c1=20*exp(-5*t).*sin(k1*t);k2=2*pi*15;c2=35*exp(-6*t).*sin(k2*t);y=c1+c2+0.2*randn(size(2*pi*t)); T = diff (t(1:2));N = length(y)-1;f = [0:(N-1) / 2] / (N*T);H = fft(y);H= H/N;H = [H(1) 2*H(2:N/2)]; plot(f,abs(H));

Nhn vo hnh trn ta thy c 2 tn s chnh l 10Hz v 15 Hz l tn s ca 2 tn hiu thnh phn.

5.2. Dng Notch Filter tch tn hiu.

Ta s dng s Simulink nh hnh di:

5.2.1.Tch ly tn hiu tn s 15HzTa chn hm truyn cho b lc Notch Filter l:

Ta thu c th t scope

Ta ly ta 11 nh A(t,y):ty

034.99

0.05816.31

0.12615.31

0.19210.42

0.2617.624

0.3263.147

0.3853.018

0.4612.398

0.5260.8279

0.5820.8069

0.6610.768

Ly Logarit t nhin tung ca cc im ta c cc im B(t, z):tz

03.5551

0.0582.7918

0.1262.7285

0.1922.3437

0.2612.0313

0.3261.1464

0.3851.1046

0.4610.8746

0.526-0.1889

0.582-0.2146

0.661-0.264

Xt 11 im B(t,z) ny tng i cng nm trn 1 ng thng.Phng trnh ng thng i qua 11 im c dng: y1 = a1+b1.tp dng phng php bnh phng cc tiu ta c h phng trnh:

y1 = 3.32-5.8t

Phng trnh ng thng qua tp hp im:y1 = 3.32-5.8t ln(z1)= 3.32-5.8t z1 = 27.66 Phng trnh ng bao bin tn hiu 15Hz l: z1 = 27.66 Vy qua b lc ta thu c tn hiu tn s 15Hz c , bin cc i 27.66.

5.2.2.Tch ly tn hiutn s 10Hz.Ta chn hm truyn cho b lc Notch Filter l:

Ta thu c th t scope:

Ta ly ta 9 nh A1(t,y):ty

0.02623.12

0.14210.56

0.257.015

0.3463.971

0.452.588

0.5481.456

0.650.9402

0.7460.5373

0.850.3411

Ly Logarit t nhin tung ca cc im ta c cc im B1(t, z):tz

0.0263.1407

0.1422.357

0.251.9481

0.3461.379

0.450.9509

0.5480.3757

0.65-0.0617

0.746-0.6212

0.85-1.0756

Xt 9 im B1(t,z) ny tng i cng nm trn 1 ng thng.Phng trnh ng thng i qua 9 im c dng: y1 = a1+b1.t

p dng phng php bnh phng cc tiu ta c h phng trnh:

y1 = t

Phng trnh ng thng qua tp hp im:y1 = tln(z1)= tz1 = 24.05Phng trnh ng bao bin tn hiu 15Hz l: z1 = 24.05 Tn hiu tn s 10Hz c .

5.3. So snh kt qu

5.3.1. Tn hiu tn s 10HzTa c th:

Ta thy tn hiu thu c qua b lc vn cn c sai s so vi tn hiu gc do c nhiu v do thng s b lc cn cha chnh xc. Tuy nhin ng bao bin th tng i bm st tn hiu gc.

5.3.2. Tn hiu tn s 15HzTa c th:

Ta thy gia tn hiu thu c qua b lc v tn hiu u vo c sai s do c nhiu v cht lng b lc cha cao. Tuy nhin ng bao bin bm kh st tn hiu u vo.

5.4. Thit k b lc bng Matlab Ngoi phng php s dng Simulink thit k b lc Notch ta c th s dng Matlab xy dng b lc. V d vi vic tch ly tn hiu tn s 10Hz:t=0:0.0001:1;a1=20*sin(2*pi*10*t);b1=exp(-5*t);a2=35*sin(2*pi*15*t);b2=exp(-6*t);for k=1:10001c1(k)=a1(k)*b1(k);c2(k)=a2(k)*b2(k);endy=c1+c2+0.2*randn(size(2*pi*t));num=[1 1 900*pi*pi];den=[2 87 900*pi*pi];w=tf(num,den); [z,t]=lsim(w,y,t);plot(t,z);axis([0 1 -40 40]);Trong : l cc hm gip thit k b lc vi cc thng s tng ng.

Ta cng thu c kt qu tng t vi vic m phng bng Simulink:

Kt lun chung n ny trnh by phng php s dng hm Fast Fourier Transform(FFT), kt hp vi s dng Notch Filter ta c th nhn dng c m hnh ton hc bc 2 ca tng tn hiu u vo t mt tn hiu tng hp, bng cch: S dng FFT xc nh tn s ca tng tn hiu thnh phn. Lc tch tn hiu bng NotchFilter. S dng phng php bnh phng cc tiu xc nh ng bao bin ca tn hiu, t xc nh c bin v h s tt dn ca tn hiu. chnh xc ca cc thng s m hnh ph thuc vo cht lng ca b lc Notch v chu nh hng nh ca nhiu. T cc thng s ny ta c th thit k c b iu khin thch hp cho tng h thng v mc ch s dng khc nhau.5.5.

Ti liu tham kho

1. Automatic Control Systems 9th Book.

2. X l s tn hiu( Phng php truyn thng kt hp vi phn mm Matlab) TS.H Vn Sung

3. Matlab & simulink dnh cho k s iu khin t ngNguyn Phng Quang4. X l tn hiu v lc s (Chng trnh tng hp v thit k cc b lc s)PGS. TS. Nguyn Quc Trung

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