You can use an active crossover. That would connect to the KEFs and whatever amp you'll use to drive your subwoofer.
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You should download the wireless app for your speakers and see what controls they give you on the sub output. If you have a choice, I'd start with the crossover at 80hz with a 24db/octave slope.
Some subs have parametric EQ (SVS Ultra does) so that you can compensate for room nodes.
The sub will have FAR lower distortion at bass frequencies than your Kefs. At 50hz the distortion of the regular LS50 is only 20db below signal level. Even at 100hz, those little midbass drivers have major distortion.
Bass management is a HT solution. For music, you should deal with it yourself. If you buy a powered sub it should come with a built in xover, and instructions on how to set it up. There's no reason to make it complicated. People were setting up subs long before there were HT processors with bass management features.
yes. no processing or crossovers needed- just a sub with the right connections and adjustments. KEF LS50- perfectly flat response through the bass region-