Tema PDS 3

Tema PDS 3

Problema 8:

N=25;

Ft=4;

Fs=20;

w=2*Ft/Fs;

h1=fir1(N-1,w,boxcar(N))

h2=fir1(N-1,w,hamming(N))

h3=fir1(N-1,w,hann(N))

h4=fir1(N-1,w,bartlett(N))

n=0:N-1;

figure(

subplot(4,1,1),stem(n,h1),title('Fereastra Dreptunghiulara'

subplot(4,1,2),stem(n,h2),title('Hamming'

subplot(4,1,3),stem(n,h3),title('Hann'

subplot(4,1,4),stem(n,h4),title('Bartlett'

Constelatia de Zerouri:

figure(

subplot(2,2,1),zplane(h1),title('Dreptunghiulara')

subplot(2,2,2),zplane(h2),title('Hamming')

subplot(2,2,3),zplane(h3),title('Hann')

subplot(2,2,4),zplane(h4),title('Bartlett')

% caracterisicile de amplitudine - frecventa normata

f

H1=fft h1,512)

H2=fft h2,512)

H3=fft h3,512)

H4=fft h4,512)

figure(

F=f*Fs

plot(F,fftshift(abs(H1)),'g',F,fftshift(abs(H2)),'r',F,fftshift(abs(H3)),'y',F,fftshift(abs(H4)),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Bartlett'

%caracteristicile de amplitudine - frecventa normata in dB

plot(f,20*log10(fftshift(abs(H1))),'g',f,20*log10(fftshift(abs(H2))),'r',f,20*log10(fftshift(abs(H3))),'y',f,20*log10(fftshift(abs(H4))),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Bartlett'

%caracteristicile de faza - frecventa normata

plot(f,fftshift(angle(H1)),'g',f,fftshift(angle(H2)),'r',f,fftshift(angle(H3)),'y',f,fftshift(angle(H4)),'b'

legend('dreptunghiulara' 'Hamming' 'Hann' 'Bartlett'

Pentru a afla atenuarea minima:

A1=20*log10(fftshift(abs(H1)))

A2=20*log10(fftshift(abs(H2)))

A3=20*log10(fftshift(abs(H3)))

A4=20*log10(fftshift(abs(H4)))

ref1=0;

ref2=0;

ref3=0;

ref4=0;

for i=1:1:512;

if A1(i)<ref1

ref1=A1(i)

end

if A2(i)<ref2

ref2=A2(i)

end

if A3(i)<ref3

ref3=A3(i)

end

if A4(i)<ref4

ref4=A4(i)

end

ref1,ref2,ref3,ref4

end

ref1 -84.6811

ref2 = -119.6655

ref3 = -112.9142

ref4 -34.3761

Castigul:

C1=abs(H1(1))

C2=abs(H2(1))

C3=abs(H3(1))

C4=abs(H4(1))

C11=abs(H1(round(512*Ft/Fs)))

C22=abs(H2(round(512*Ft/Fs)))

C33=abs(H3(round(512*Ft/Fs)))

C44=abs(H4(round(512*Ft/Fs)))

C111=abs(H1(round(512*1/2)))

C222=abs(H2(round(512*1/2)))

C333=abs(H3(round(512*1/2)))

C444=abs(H4(round(512*1/2)))

C1 =1.0000

C2 =1

C3 = 1

C4 = 1.0000

C11 = 0.5322

C22 = 0.5330

C33 0.5331

C44 = 0.5502

C111 8.7623e-004

C222 1.3181e-004

C333 =2.2329e-004

C444 = 0.0191

Problema 1:

%Problema 1

Fs=20;

F=8;

z1=2/exp(j*pi/3);

z2=0.7;

z3=exp(j*2*pi*F/Fs);

z=[z1;conj(z1);1/z1;conj(1/z1);z2;1/z2;1;-1;z3;conj(z3)];

p=poly(z)

k=0.709/abs(polyval(p,exp(j*pi/4)))

h=p*k

n=0:length(h)-1

figure(

stem(n,h

figure(

zplane z)

H=fft h,512)

w=-pi:2*pi/512:pi-2*pi/512;

figure(3),plot(w,20*log10(fftshift(abs(H)))),grid

figure(4),plot(w,fftshift(angle(H))),grid

c1=abs(polyval(h,1))

c2=abs(polyval(h,exp(j*pi/2)))

c3=abs(polyval(h,exp(j*pi)))

p = 1.0000 -3.0105 4.0822 0.9299 -8.1111 0 8.1111 -0.9299 -4.0822

3.0105 -1.0000

c1 = 2.2204e-016

c2 =3.0221

c3 =6.4832e-016

Problema 19:

%Filtrul este un FTJ

%N-impar

%Filtrul va fi de ordinul 1;

w=pi/5

N=43;

%f=-(N-1)/2*w;

h1=fir1(N-1,w/(pi),blackman(N))

h2=fir1(N-1,w/(pi),hamming(N))

h3=fir1(N-1,w/(pi),hann(N))

h4=fir1(N-1,w/(pi),triang(N))

n=0:N-1

figure(

subplot(4,1,1),stem(n,h1)

subplot(4,1,2),stem(n,h2)

subplot(4,1,3),stem(n,h3)

subplot(4,1,4),stem(n,h4)

figure(

subplot(2,2,1),zplane(h1)

subplot(2,2,2),zplane(h2)

subplot(2,2,3),zplane(h3)

subplot(2,2,4),zplane(h4)

f = -0.5:1/512:0.5-1/512

H1=fft h1,512)

H2=fft h2,512)

H3=fft h3,512)

H4=fft h4,512)

figure(

plot(f,fftshift(abs(H1)),'r',f,fftshift(abs(H2)),'y',f,fftshift(abs(H3)),'g',f,fftshift(abs(H4)),'b'

legend('Blackman' 'Hamming' 'Hann' 'triang'

figure(

w1=-pi:2*pi/512:pi-2*pi/512

plot(w1,abs(H1),'g',w1,abs(H2),'b',w1,abs(H3),'r',w1,abs(H4),'y'

legend('Blackman' 'Hamming' 'Hann' 'triang'

figure(

plot(w1,fftshift(angle(H1)),'g',w1,fftshift(angle(H2)),'b',w1,fftshift(angle(H3)),'r',w1,fftshift(angle(H4)),'y'

legend('Blackman' 'Hamming' 'Hann' 'triang'

Problema 26:

%folosim fir1

clear all

N=51

w1=0.25*pi

w2=0.5*pi

w3=0.8*pi

wi=[w1,w2];

wii=[w3,0.99*pi]

h11=fir1(N-1,wi/(pi),boxcar(N))

h12=fir1(N-1,wi/(pi),hamming(N))

h13=fir1(N-1,wi/(pi),hann(N))

h14=fir1(N-1,wi/(pi),triang(N))

h21=fir1(N-1,wii/(pi),boxcar(N))

h22=fir1(N-1,wii/(pi),hamming(N))

h23=fir1(N-1,wii/(pi),hann(N))

h24=fir1(N-1,wii/(pi),triang(N))

h1=0.4*h11+h21

h2=0.4*h12+h22

h3=0.4*h13+h23

h4=0.4*h14+h24

n=0:N-1

figure(

subplot(4,1,1),stem(n,h1)

subplot(4,1,2),stem(n,h2)

subplot(4,1,3),stem(n,h3)

subplot(4,1,4),stem(n,h4)

figure(

subplot(2,2,1),zplane(h1)

subplot(2,2,2),zplane(h2)

subplot(2,2,3),zplane(h3)

subplot(2,2,4),zplane(h4)

f = -0.5:1/512:0.5-1/512

H1=fft h1,512)

H2=fft h2,512)

H3=fft h3,512)

H4=fft h4,512)

figure(

plot(f,fftshift(abs(H1)),'r',f,fftshift(abs(H2)),'y',f,fftshift(abs(H3)),'g',f,fftshift(abs(H4)),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'

figure(

plot(f,20*log10(fftshift(abs(H1))),'r',f,20*log10(fftshift(abs(H2))),'y',f,20*log10(fftshift(abs(H3))),'g',f,20*log10(fftshift(abs(H4))),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'

figure(

plot(f,fftshift(angle(H1)),'r',f,fftshift(angle(H2)),'y',f,fftshift(angle(H3)),'g',f,fftshift(angle(H4)),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'

%folosind fir2

fe=[0 0.3 0.5 0.7 1]

m=[0 0 0.4 0 1 ]

h1=fir2(N-1,fe,m,boxcar(N))

h2=fir2(N-1,fe,m,hamming(N))

h3=fir2(N-1,fe,m,hann(N))

h4=fir2(N-1,fe,m,triang(N))

n=0:N-1

figure(

subplot(4,1,1),stem(n,h1)

subplot(4,1,2),stem(n,h2)

subplot(4,1,3),stem(n,h3)

subplot(4,1,4),stem(n,h4)

figure(

subplot(2,2,1),zplane(h1)

subplot(2,2,2),zplane(h2)

subplot(2,2,3),zplane(h3)

subplot(2,2,4),zplane(h4)

f = -0.5:1/512:0.5-1/512

H1=fft h1,512)

H2=fft h2,512)

H3=fft h3,512)

H4=fft h4,512)

figure(

plot(f,fftshift(abs(H1)),'r',f,fftshift(abs(H2)),'y',f,fftshift(abs(H3)),'g',f,fftshift(abs(H4)),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'

figure(

plot(f,20*log10(fftshift(abs(H1))),'r',f,20*log10(fftshift(abs(H2))),'y',f,20*log10(fftshift(abs(H3))),'g',f,20*log10(fftshift(abs(H4))),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'

figure(

plot(f,fftshift(angle(H1)),'r',f,fftshift(angle(H2)),'y',f,fftshift(angle(H3)),'g',f,fftshift(angle(H4)),'b'

legend('Dreptunghiulara' 'Hamming' 'Hann' 'Triung'