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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('
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('
% 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' '
%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' '
%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' '
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'
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