townini4

PIERWSZE:
LAGRANGE:
godzina = [5,6,8,11]
temp = [ -2,3,7,10]

y = [5:0.1:11]

for g = 1:61
    A = ones (1,4)
    B = ones (1,4)
    for i = 1:4
        for k = 1:4
            if (i~=k)
                A(i)=A(i)*(y(g)-godzina(k))
                B(i)=B(i)*(godzina(i)-godzina(k))
            end
        end
     L(i,g)=A(i)/B(i)
    end

end

T=zeros(1,61)

for g = 1 : 61
    for i = 1 : 4
        T(g)=T(g)+temp(i)*L(i,g)
    end
end

.....................................
NEWTON:
godzina = [5,6,8,11]
temp = [ -2,3,7,10]
god = [5:0.1:11]

N=4
d(:,1)=temp';
for j=2:N
    for i=j:N
        d(i,j)= ( d(i-1,j-1)-d(i,j-1)) / (godzina(i-j+1)-godzina(i));
    end
end
a = diag(d)';

A2 = ones (1,61)
for i=1:61
    for k= 1 :4
        A2(i)=A2(i)*(god(i)-godzina(k))
    end
end

for g= 1:61
    T2(g)=-2+(5*(god(g)-5))-((god(g)-5)*(god(g)-6))+((4/30)*(god(g)-5)*(god(g)-6)*(god(g)-8))
end


hold all
plot(god,T2)
plot(god,T)
plot(godzina,temp,'*')
..............................................................................
DRUGIE:
x=(-5:0.01:5);
y=1./(1+x.^2);
xk=-5:1:5;
yk=1./(1+xk.^2);
yi= interp1(xk,yk,x,'linear')



xk = xk';
yk = 1./(1+xk.^2);
cs = spline( xk', [0 yk' 0] );
y3 = ppval( cs, x );
plot(x,y,xk,yk,'o',x,yi,'r--',x,y3);

....................................................................
TRZECIE:
clear all
f1=50;
f2=150;
f3=10000;
for n=0:9999
    x(n+1)=sin((2*pi*f1*n)/f3)+0.5*sin((2*pi*f2*n)/f3);
end
R=5;
N=10000;
xr=zeros(1,N);
for n=0:R:N-1
    xr(n+1)=x(n+1);
end
M=1000;
for m=-M:1:M
    h(m+M+1)=(sin((pi*m)/R))/((pi*m)/R);
end
h(M+1)=1;

xe=conv(xr,h);

for n=2*M+1:12000-2*M
    xem(n-2*M)=xe(n);
end
for n=M+1:N-M
    xm(n-M)=x(n);
end

........................................
function [  ] = lab4_3( R, M )
%UNTITLED Summary of this function goes here
%   Detailed explanation goes here
f
1 = 50;

f2 = 150;

fs = 10000;

for n = 0:9999;

    x(n+1) = sin(2*pi()*f1 * n / fs) + 0.5*sin(2*pi()*f2*n/fs);

end

plot(x)

hold on

input('')

xr(10000)=0;

for n=0:R:9999

    xr(n+1) = x(n+1);

end

plot(xr, 'g')

hold off

input('')

h(M+1)=1;

for m=1:M

    h(m) = sinc(pi()*(M+1-m)/R);

    h(m+M+1) = sinc(pi()*m/R);

end

plot(h)

input('')

xe=conv(xr, h);

xe2 = xe(2*M:length(xe)-2*M);

x2 = x(M:length(x)-M);

plot(xe2-x2, '-')

input('')

%plot(x2)

%hold on;

%plot(xe2, '-g');

% length(x2)

% length(xe2)

%plot(abs(abs(xe2) - abs(x2)), '.');

%plot(h);

%plot(xd)

end


..............................
fp=10000;
f1=50;
f2=150;

for i = 1:10000
    iks(i)=sin((2*pi*f1*i)/fp)+1/2*sin((2*pi*f2*i)/fp);
end

R1=5;
R2=10;
R3=25;
iks1=iks;
iks2=iks;
iks3=iks;

for i = 1:10000
    if (rem(i,R1)~=0)
        iks1(i)=0;
    end
end
for i = 1:10000
    if (rem(i,R2)~=0)
        iks2(i)=0;
    end
end
for i = 1:10000
    if (rem(i,R3)~=0)
        iks3(i)=0;
    end
end

M=1000;
for m=-M:M
    h1(m+M+1)=(sin((pi*m)/R1))/((pi*m)/R1);
end
h1(M+1)=1;

for m=-M:M
    h2(m+M+1)=(sin((pi*m)/R2))/((pi*m)/R2);
end
h2(M+1)=1;

for m=-M:M
    h3(m+M+1)=(sin((pi*m)/R3))/((pi*m)/R3);
end
h3(M+1)=1;

 splot1 = conv(iks1,h1);
 splot2 = conv(iks2,h2);
 splot3 = conv(iks3,h3);

 splot1 = splot1(2*M:end-2*M);
 splot2 = splot2(2*M:end-2*M);
 splot3 = splot3(2*M:end-2*M);

iks=iks(M:end-M);
iks1=iks1(M:end-M);
iks2=iks2(M:end-M);
iks3=iks3(M:end-M);


subplot(3,1,1); plot(iks)
subplot(3,1,2); plot(iks3)
subplot(3,1,3); plot(splot3)


zaba=zeros(1,N);

   for i=0:N-1
       for k =0:(N/R1-1)
           zaba(i+1)=zaba(i+1)+iks(k*R1+1)*(sinc((i-k*R1)/R1));
       end
   end


....................................................................................
function f = newton(x, y, p)

n = length(x);
d(:,1)=y';
for j=2:n
    for i=j:n
        d(i,j)= ( d(i-1,j-1)-d(i,j-1)) / (x(i-j+1)-x(i));
    end
end
a = diag(d)';

Df(1,:) = ones(size(p));
c(1,:) = a(1)*ones(size(p));
for j = 2 : n
   Df(j,:)=(p - x(j-1)) .* Df(j-1,:);
   c(j,:) = a(j) .* Df(j,:);
end
f=sum(c);
....................................................................................
function y=Lk(x,xk,k)

n=length(x)-1;
ni=length(k);
L=ones(n+1,ni);
for i=0:n
    for j=0:(i-1)
        L(j+1,:)=L(j+1,:).*(k-x(i+1))/(x(j+1)-x(i+1));
    end

    for j=i+1:n
        L(j+1,:)=L(j+1,:).*(k - x(i+1))/(x(j+1)-x(i+1));
    end
end
y = xk * L;
....................................................................................