lab1_2

clc;
clear;
T = 5;

x  = 0:.01:T;

[y]  = textread('f6.txt', '%f');

N = length(y);

z = double(zeros(size(y)));



for k = 1:N
    re = 0.0;
    im = 0.0;
    for m = 1:N
        re = re + y(m) * cos(2 * pi * (k - 1) * (m - 1) / N) / N;
        im = im + y(m) * cos(2 * pi * (k - 1) * (m - 1) / N) / N;
    end
    z(k) = sqrt(re^2 + im^2);
end

figure
plot(x, z, 'b')
title('dft')
xlabel('x')
ylabel('|c(x)|')
grid on


mx = [];
eps = 1e-6;
for k = 2:N/2
    if (z(k) > z(k-1) + eps) && (z(k) > z(k+1) + eps)
        mx(end + 1) = x(k);
    end
end

mx

M = 4 + numel(mx);
A = zeros(M, M);
B = zeros(M, 1);

for k = 1:N
    v = zeros(M);
    t = k / 100;
    v(1) = t^3;
    v(2) = t^2;
    v(3) = t;
    for i = 1:numel(mx)
        v(3 + i) = sin(2 * pi * t * mx(i));
    end
    v(M) = 1.0;
    for i = 1:M
        for j = 1:M
            A(i,j) = A(i,j) + v(i) * v(j);
        end
        B(i) = B(i) + v(i) * y(k);
    end
end


a = A^(-1)*B;

func = zeros(N,1);
for k = 1:N
    v = zeros(M);
    t = k / 100;
    v(1) = t^3;
    v(2) = t^2;
    v(3) = t;
    for i = 1:numel(mx)
        v(3 + i) = sin(2 * pi * t * mx(i));
    end
    v(M) = 1.0;
    for i = 1:M
        func(k) = func(k) + a(i) * v(i);
    end
end

figure
plot(x, y, 'r', x, func, 'k')
xlabel('t')
ylabel('y(t)')
title('function')
grid on