I have a problem dealing with a real signal in time domain or in frequency domain when I need to do some processing on it in the dual or other domain via FFT or IFFT.
I find myself dealing with a complex signal and after doing the processing and wanting to go back to the original domain I end up having a complex signal when I really want to deal with a real signal only.
Why is this happening? How can I deal with it?
You started with a real signal but it was always complex it was just those parts were zero. Now after doing some computation you have a complex real signal. Now you can just spit out the magnitude of each point but you will lose information, a lot of the time it does not matter. If it is a rf communication system you need to tx/Rx the complex wave.
You didn't exactly "start with a real signal". What you started with, was differential equations for inductors, capacitors, and resistors in an equivalent to your real circuit. Those simultaneous differential equations become linear equations when you use complex conductances/impedances like "j⍵C" and "j⍵L" and you need both the real parts and imaginary parts to track the phase of your output results for all those frequency components.
This is happening because you are using a set of simple linear equations instead of coupled differential equations.
The resulting signals can be interpreted with both AC amplitudes, and phases, and all that takes is a conversion from Cartesian (real and imaginary axes) to polar (phase and amplitude) representation. And, summation over any and all frequencies under consideration, because your results are one-frequency-at-a-time depictions.
