Alf P. Steinbach wrote: > * Steve Holden: >> Alf P. Steinbach wrote: >>> Just as a contribution, since someone hinted that I haven't really >>> contributed much to the Python community. >>> >>> The [simple_sound] code will probably go into my ch 3 at <url: >>> http://tinyurl.com/programmingbookP3>, but sans sine wave generation >>> since I haven't yet discussed trig functions, and maybe /with/ changes >>> suggested by you? >>> >> I wouldn't hold back on the sine wave just because it would represent a >> "forward reference". That's OK sometimes. Why not just put a comment in >> to the effect that "The sine wave is created using a function from the >> math module, which we'll be looking at in ..."? >> >> Since the sine is the basis for all other waveforms its omission would >> seem more than a little strange to anyone knowledgeable about audio, for >> example. > > I don't know very much if anything about audio. For example, in the code > what I called "sawtooth" wave is really "triangle" wave. The sawtooth is > simpler, what I called "linear" in the code. > > And if you wonder, I was just checking the terminology now before > starting to write it up... Perhaps should have done that before posting > code. But once I got the idea of posting it I just posted it. > > Anyway, as I recall any wave can be decomposed into sine waves, or > square waves, or almost whatever kind of waves. Think about a square > wave of frequency f and one of frequency 3f and perhaps third the > amplitude (not sure), combined that's already a good start on a sine > wave. With some ugly staircasing but hey. And as a matter of programming > practicality, a triangle wave sounds almost like a sine wave. It's just > a little more edgy or "hairy", a slight buzz. > It's not clear to me that you can approximate any waveform with a suitable combination of square waves, though I admit the idea has intuitive appeal. But I know beyond a shadow of a doubt from my education that any periodic function with a fundamental frequency f can be approximated to whatever desired accuracy by the sum of sine and cosine waves of frequencies Nf (N = 0, 1, 2, 3, ...) of appropriate amplitudes (the frequency 0 component allows you to insert a "DC shift" for waveforms that aren't symmetrical about zero). I seem to remember the Fourier's theorem was the fundamental proof.
There is a very pretty discussion of all this, if you are mathematically inclined, in http://press.princeton.edu/books/maor/chapter_15.pdf with a specific example for the sawtooth waveform. I would definitely recommend renaming the waveforms you *do* use to conform with accepted terminology. This will reduce reader confusion. regards Steve -- Steve Holden +1 571 484 6266 +1 800 494 3119 PyCon is coming! Atlanta, Feb 2010 http://us.pycon.org/ Holden Web LLC http://www.holdenweb.com/ UPCOMING EVENTS: http://holdenweb.eventbrite.com/ -- http://mail.python.org/mailman/listinfo/python-list
