% sum of three real Fourier sinusoids plus noise:

    n = (0:199).' ;
    s = 4.7*cos(0.12*pi*n - 1.3) + ...
        3.8*cos(0.19*pi*n + 0.8) + ...
        5.1*cos(0.23*pi*n + 2.4) + ...
        2.0*randn(size(n)) ;

    plot(n,s)

    S = fft(s) ;
    bar(n,abs(S)) , grid

% same sinusoids, no noise:

    n = (0:199).' ;
    s = 4.7*cos(0.12*pi*n - 1.3) + ...
        3.8*cos(0.19*pi*n + 0.8) + ...
        5.1*cos(0.23*pi*n + 2.4) ;

    plot(n,s)

    S = fft(s) ;
    bar(n,abs(S)) , grid
    bar(n, angle(S).*(abs(S)>1e-10)) , grid

% change above to non-Fourier sinusoids:

    n = (0:199).' ;
    s = 4.7*cos(0.12321*pi*n - 1.3) + ...
        3.8*cos(0.19642*pi*n + 0.8) + ...
        5.1*cos(0.23419*pi*n + 2.4) ;

    plot(n,s)

    S = fft(s) ;
    bar(n,abs(S)) , grid

% single complex non-Fourier sinusoid:

    n = (0:19).' ;
    f1 = (0 : 0.05 : 0.95).' ;
    f2 = (0 : 0.001 : 0.999).' ;
    s = exp(j*0.317*2*pi*n).' ;

    stem( f1, abs(fft(s)), 'k' ) ;

    hold
    plot( f2, abs(fft(s,1000)) ) ;