lab1

clc;
clear;
T = 5;
x  = 0: .01 : T;
[y]  = textread('f8.txt', '%f');
N = length(y);

c = complex(zeros(size(y)));

for k = 1:N
    for m = 1:N
        c(k) = c(k) + y(m)*(exp((-1i*2*pi*(k-1)*(m-1)) / N)/N);
    end
end


z = abs(c);

extremums = [];
eps = 1e-5;
for k = 3:N/2
    if (z(k) > z(k-1) + eps) && (z(k) > z(k+1) + eps) && (z(k) > z(k-2) + eps) && (z(k) > z(k + 2) + eps)
        extremums(end + 1) = x(k);
    end
end

extremums

M = length(extremums) + 4;
A = zeros(M, M);
B = zeros(M, 1);



func = {@(t) t.^3, @(t) t.^2, @(t) t};
for k = 1:length(extremums)
    func(end + 1) =  {@(t) sin(2*pi*extremums(k)*t*100/T)};
end
func(end + 1) = {@(t) 1};

for p = 1:M
    for q = 1:M
        for k = 1:N
            A(p,q) = A(p,q) + func{p}(x(k)) * func{q}(x(k));
        end
    end
    for k = 1:N
        B(p) = B(p) + y(k) * func{p}(x(k));
    end
end


a = A^(-1)*B;


newY = zeros(N,1);
for k = 1:N
    for i = 1:M
        newY(k) = newY(k) + a(i) * func{i}(x(k));
    end
end

figure
plot(x, y, 'r', x, newY, 'k')
xlabel('x')
ylabel('y(x)')
title('Function')
grid on

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