I used to own and use several of the Alpine PXA-H700 digital processors in my car audio systems. If you have one of the H700's with a quiet/no-hiss Analog input, I would just use the DX-90's Line Output to the H700's Analog Input. It is equivalent to the 2-volt Redbook Standard and is plenty "hot" to supply a very clean signal to the H700. If you have one of the H700's that suffers from the Analog Input "noise floor/hiss" issue, then you may need to get an S/PDIF Coaxial-to-Toslink Optical converter as already suggested and use the Toslink Optical input on the H700. This type of converter needs power to operate.
The Alpine PXA-H700 does all of it's processing/DSP (Parametric & Graphic EQ, Digital Delay "time alignment", adjustable Crossover Network) in the digital domain at 16-bit/48kHz, so any other sample rate that is fed to the processor will be down-sampled to that. And unfortunately, as good as the PXA-H700 DACs are, they are no match for the newer Sabre chips in the DX-90. That said, your system will not sound any worse than it is now, and should sound even better by feeding it the very clean output of the DX-90.
I'm planning to do something similar, but using the Arc Audio PS8 DSP which has a coaxial input. Good luck.