The DSP was cool until it wasn't. It was a bit of a boondoggle that NeXT got stuck with for a while. The initial thinking as this stuff was being developed was the DSP would be great for audio. It's hard to remember this, but you cant really even play an MP3 on most black NeXT hardware. There is one app (that was removed at the time because of MP3 patent issues) that could do it on 68040 turbo systems (33mhz) ok. Some got it to kind of work on the 25mhz 040 as well, but you better be not running anything else. It would not work on the original l 68030 chips.
Anyway, the initial machines were being worked on the CPUs were still going to be pretty anemic in that regard (68020, 68030), so the 56001 would help with audio processing in part (and I believe escort later used it for their radar detectors touting NeXT technology, lol). It could do a bit more than that and there certainly were many cool apps that took advantage of itI believe there were even a couple of boards that hand multiple 56001's on it for doing really serious MusicKit stuff. For example, the old demo Mandelbrot.app could be run on the 030 or the 56001, and it would go way faster on the 56001.
The problem came as CPUs got way faster, the 56001 kind of stuck around for legacy app reasons and it was pretty slow and kind of was just extra expense. It went away when NeXT moved to intel and other processors.
What not many people remember, NeXT had 2 audio kits. One was the sound kit, which has somewhat morphed with the Mac into a much more mature kit. With it there were a few cool things at the time. NeXT had a native "CD" quality sound file format, and you could also compress losslessly to about half the size. Some of that playback and compression could be offloaded to the DSP. It was buggy as hell. But way before the iPod, I got hold of one of the first digital rip apps on NeXTstep. It could pump audio purely over the SCSI bus (back then the only way your PC played CD was over a by pass cable to your speakers and ripping audio was still copy-protected then, and little known, one of the first GUI rip apps was on NeXT). I remember ripping my CDs to the .snd files, compressed to half size and playing them off my magneto optical drive which could have well over 100 tracks on it. Kind of the 100 songs in your pocket thing. Getting the compression down in real time was VERY buggy from the rip and the DSP there was always iffy. They may have patched some of the bugs later, but by that time they were moving away from using the DSP as they saw it as a bit of a boat anchor.
Anyway, there was a super impressive pro
MusicKit as well. It was SUPER cool. They ended up opensourcing and giving it to
Stanford, which frankly let it languish and kind of die, which is a shame. It let you do really amazing synth music, with some amazing professional scoring apps, and it could employ the DSP quite well.
Anyway, the original M56001 came with all the black hardware, and basically just was omitted when white hardware came out. Although I do remember even for intel hardware, someone came out with a multiDSP board for more sophisticated MusicKit work.
One of the early interesting uses was basically the governments 3 letter agency used early NeXT for their "capture everything" tech that later became quite the scandal multiple times. NeXT sold around 50k units officially, but there was a bit of a black hole in numbers to those agencies, so there are probably a touch more than the official touted numbers. But, the DSP usage back when one would capture audio via glorified modem technology, faxes (those were still a thing and used the DSP to let you have cheaper fax modems hooked to a NeXT which could be network shared back then and was helpful for processing some of that data, no doubt), and electronic communications etc.
Anyway, not sure if that answered your question, but that's the top of head meandering recollection...it's been a bit of a while so of course, take it with grains of sand on dimming memory.
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