clear all;
N = 32;
L= 32;


%macierz F transformaty
for(n=0:N-1)
    for(m=0:N-1)
      F(n+1,m+1) = (1/sqrt(N))*cos((2*pi/N)*n*m)-i*(1/sqrt(N))*sin((2*pi/N)*n*m);
    end
end

disp("czy F jest ortogonalna?")
FF =F*F';
real(FF(1:5,1:5))       %tak jest


%__________________________dla sygnalu sin____________________
if(0)
    %sygnal wyslany sinusy
    L = 32;
    x3 = zeros(32,1);
    for(n=0:31)
        x3(n+1)= sin(2*pi*2*n/L)+sin(2*pi*6*n/L);
    end

    %plot(x3,'r');
    %pause;

    X = F*x3;
    X_obrazek = 20*log(abs(X));
    plot(X_obrazek);
    title("widmo gestosci mocy");
    pause;

    x3_1 = inv(F)*X;     %x~
    x3_1_2 = inv(F.')*X;   %x~~

    %czy wyniki sa takie same co do bledow numerycznych
    errorx3_1_to_x = max(abs(x3-x3_1))
    errorx3_1_2_to_x = max(abs(x3-x3_1_2))

    if(x3_1 == x3_1_2)
        disp("macierze sa takie same");
    else
        disp("macierze sa inne")
    end
    figure; subplot(311);plot(1:L,x3,'-r');title("nadany");subplot(312);plot(1:L,x3_1,'-b');title("odebrany synteza 1");
    subplot(313);plot(1:L,x3_1_2,'-b');title('odebrany synteza 2');

end

%_____________________sygnal exp______________________
if(0)
    L = 32;
    x3 = zeros(32,1);
    for(n=0:31)
        x3(n+1)= exp(-i*2*pi*2*n/L)+exp(-i*2*pi*6*n/L);
    end

    %plot(x3,'r');
    %pause;

    X = F*x3;
    X_obrazek = 20*log(abs(X));
    plot(X_obrazek);
    title("widmo gestosci mocy");
    pause;

    x3_1 = inv(F)*X;     %x~
    x3_1_2 = inv(F.')*X;   %x~~

    %czy wyniki sa takie same co do bledow numerycznych
    errorx3_1_to_x = max(abs(x3-x3_1))
    errorx3_1_2_to_x = max(abs(x3-x3_1_2))

    if(x3_1 == x3_1_2)
        disp("macierze sa takie same");
    else
        disp("macierze sa inne")
    end
    figure; subplot(311);plot(1:L,x3,'-r');title("nadany");subplot(312);plot(1:L,x3_1,'-b');title("odebrany synteza 1");
    subplot(313);plot(1:L,x3_1_2,'-b');title('odebrany synteza 2');


end
%______________________dla y3__________________________
if(0)
    load("h.mat");
    L = 32;
    x3 = zeros(32,1);
    for(n=0:31)
        x3(n+1)= sin(2*pi*2*n/L)+sin(2*pi*6*n/L);
    end
    h = h';                             %nie umiem tego conv
    X3 = toeplitz(x3, zeros(1,32));
    y = X3*h;

    X = F*y;
    X_obrazek = 20*log(abs(X));
    plot(X_obrazek);
    title("widmo gestosci mocy");
    pause;

    y3_1 = inv(F)*X;     %x~
    y3_1_2 = inv(F.')*X;   %x~~

    %czy wyniki sa takie same co do bledow numerycznych
    errory3_1_to_y = max(abs(y-y3_1))
    errory3_1_2_to_y = max(abs(y-y3_1_2))

    if(y3_1 == y3_1_2)
        disp("macierze sa takie same");
    else
        disp("macierze sa inne")
    end
    figure; subplot(311);plot(1:L,y,'-r');title("nadany");subplot(312);plot(1:L,y3_1,'-b');title("odebrany synteza 1");
    subplot(313);plot(1:L,y3_1_2,'-b');title('odebrany synteza 2');

end


%_____________________dla random_______________________
if(1)
    rs = randn(32,1);
    %plot(rs);

    RS=F*rs;            %to jest to co jest podobne w F do sygnalu rs
    rs1=inv(F)*RS;
    rs2=inv(F.')*RS;
    X_obrazek = 20*log(abs(RS));
    plot(X_obrazek);
    title("widmo gestosci mocy");
    pause;
    %czy wyniki sa takie same co do bledow numerycznych
    error_rs1_to_rs = max(abs(rs-rs1))
    errorr_rs2_to_re = max(abs(rs-rs2))

    if(rs1 == rs2)
        disp("macierze sa takie same");
    else
        disp("macierze sa inne")
    end
    figure; subplot(311);plot(1:L,rs,'-r');title("nadany");subplot(312);plot(1:L,rs1,'-b');title("odebrany synteza 1");
    subplot(313);plot(1:L,rs2,'-b');title('odebrany synteza 2');


end