Alf P. Steinbach wrote: > * Steve Holden: [...] > With the goal of just a rough approximation you can go about it like this: > > 1. Divide a full cycle of the sine wave into n intervals. With > sine wave frequency f this corresponds to n*f sample rate for digital > representation. > > 2. Each interval will be approximated by a rectangular bar extending > up to or down to the sine wave. As it happens this (the bar's > height) is > the sample value in a digital representation. > > 3. In the first half of the cycle, for each bar create that bar as > a square wave of frequency f, amplitude half the bar's height, and > phase > starting at the bar's left, plus same square wave with negative sign > (inverted amplitude) and phase starting at the bar's right. And voilà, > not only this bar generated but also the corresponding other-way > bar in > second half of cycle. > > 4. Sum all the square waves from step 3. > > 5. Let n go to infinity for utter perfectness! :-) > > And likewise for any other waveform. > > After all, it's the basis of digital representation of sound! > > I'm sorry, but this is merely hand-waving. It looks appealing, but there's no rigor there.
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
