Compute real signal from a discrete analytic signal
@user85858302: If designing a complex-valued bandpass filter is the solution to your problem, you can design such a filter without using the Hilbert transform. Start by using your favorite method for designing a real-valued N-tap FIR lowpass filter whose one-sided bandwidth is B Hz. That will give you N real-valued coefficients. Next, multiply those coefficients by a complex exponential whose frequency is Fc Hz. (Fc must be sufficiently less than half your data’s Fs sample rate.) That will produce N complex-valued coefficients that can be used in a tapped-delay line FIR filter block diagram. The complex-valued bandpass filter will have frequency response whose center frequency is Fc Hz and a bandwidth of 2B Hz.  Model this whole process in software to demonstrate what I'm sayin' here.

For those readers interested in both real-valued and complex-valued FIR filters, I suggest you have look at the following blog. You may well learn something new about FIR filters. http://www.dsprelated.com/showarticle/808.php