# Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by

$$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\omega)$$

How can I obtain the real part of the Fourier transform?

i have simulated this by octave here:

>> w=[1:100];
>> Im_X=sin(2.*w)+sin(3.*w);
>> plot (Im_X);


Is it possible to solve in by the Octave/Matlab?