I love Körner's book: it is amazing, interesting, accurate, his personality shines through . . . . I spent quite a bit of time with it when we had debates about some of the technical issues underlying the machine. This book likely isn't the place to start your study of fourier methods, but it is THE place to end!
I had forgot about the Sum Some Sines .... that will come out ... it is a program on the processing language that lets you play with adding sines. It isn't a simulation of the machine, but it is fascinating and instructive. We choose not to release it with the machine vids.
The other vids will detail "how it works." In the next two we show the steps in synthesis and analysis, and the last on its operations details setting for sines or cosines, the pen mechanism, etc. The book also goes over this -- as you note the PDF is free. There is a direct download at the site, also a torrent. Two vids detailing what's in the book likely come out tomorrow and the day after . . . . Bill