When you purchase an LFR you're getting a DSP (Digital Signal Processor) included as well. What is the difference between that and an amp or Axiom's ADA1000?

The DSP does not include amplification so you can't connect it directly to the speakers. What it does do is process per-channel audio from your preamp into separate front and back signals (or 5 signals for actives) which then need to be fed into conventional audio amplifier channels.

One interesting option that Axiom offers is to build the DSP circuitry for a non-active LFR into a 4-channel ADA1000 amplifier, giving a good cost saving because the two components can share power supply and chassis. That allows you to connect directly from pre-amp to the DSP/amp box, and from the DSP/amp box to the speakers.

Thanks for that! Are the other speakers that don't have a DSP, analog then?

All other speakers can be connected directly to your receiver. They are called passive speakers.

Technically all speakers are analog. In passive speakers, the signals to the various drivers are sorted (filtered) using analog components. These components reside inside the speaker. In active speakers, the signals to the various drivers are sorted digitally or electronically. The superior method is digital. In the active LFR1100s, the digital methods reside in the DSPs.

Thanks for the answer. I think I got it figured out. DSP Box = more processing power = more independent sound signals = more money = upset wife? We'll see.