What is the meaning of imaginary values in the time domain?
Imaginary values in the time domain simply mean that you actually have two signals, the real-part and the imaginary part. If you start out with a real-valued signal, take the Fourier transform, do some processing in the frequency domain, then transform back, and you end up with a complex-valued signal, then 9 out of 10 times you've done something wrong (or, if the imaginary part is very small, it is numerical noise due to round-off errors). In other words, in most cases the frequency domain processing should not make your originally real-valued time domain signal complex-valued, i.e. it should retain the conjugate symmetry of the signal's Fourier transform.