'Joe Shmoe's' comments above are good (I used to be in pro-audio too).
The trouble with all sorts of woodworking machines is that the noise comes mostly from cutter meeting wood - something you can't really soundproof directly. If your machine has thin metal panels AND there's room inside you can try the following strategy to help:
Get some 'Flashband' bitumen sheet-lead substitute (for roofing repairs). Stick it to the inside of the panels (outside works just as well, but it's a bit sticky and will look rather unsightly. It doesn't have to cover the panel completely, just a large-ish part of it. I use it inside computer casings to good effect, to reduce fan and hard disk noise. The idea is it damps resonances set up by motor and blade, and stops the panel acting like a drumskin.
You can go a bit further by putting Rockwool or fibreglass inside (soaks up sound), but don't expect miraculous results. Soundproofing is all about blocking small gaps and preventing transmission of sound through the structure, as well as absorbing it. Nobody wants to work in a hermetically sealed garage, especially in the summer, but door seals in particular will have a huge effect.
You don't mention the roof - if it's thin metal sheet (coil coated stuff as the cladding on DIY sheds etc.), it too will transmit sound pretty well. Old-style corrugated asbestos cement sheets will probably give the best results (tiles have gaps between them!), but if you do have a tiled roof, putting Rockwool tightly between the rafters will both improve the insulation and do a lot to deaden escaping sound (foil-faced will be best).
There's no cheap nor easy answer to this, only attention to detail.
The other thing is the PR aspect: we don't get to choose our neighbours, but you might defuse problems by explaining what you're doing, and possibly even making them something small as a present. You never know - you might end up with a commission!
HTH,
S.
