Analog in - digital processing - analog out.
Okay, so what is the quality of the A/D and D/A conversion? I sort of have a problem with these types of DSP-based crossovers. While it is true they are way superior in flexibility to analog ones, using them means every source signal before the crossover is inevitably converted to digital. This diminishes the impact of quality source components, especially analog ones, on sound quality.
For example, if you own a pristine condition LP or R2R tape made through an entirely analog process, with a DSP-based crossover before the speakers this signal would first be converted to digital and then back to analog. While modern-day ADCs and DACs have reached their zenith, something will always be lost. What is the point in keeping these analog mediums if they're converted to digital every time you play them?
On the other hand, if you own a DSD-capable DAC and then run it's analog outputs into a DSP-based crossover, the DSD argument becomes irrelevant because no doubt, the crossover operates in PCM. More than that actially, DSP-based crossovers utilise SRCs (sample-rate converters) which set the sampling rate to whatever frequency is required by the software within the DSP. It is usually 96 kHz. Even if we are not talking about DSD, high-end PCM-only DACs become a component that is a lot less important when a digital crossover is thrown in the mix.
One might argue that a properly set-up DSP crossover yields benefits greater than what a good high-end DAC would, or other source components for that matter, but that being the case, you could easily do without all of these components then - run your PC or a BDP straight into the crossover and you're done. You'd be eliminating one cycle of D/A and A/D conversion that way.
It is just how I feel about it.