* Steve Holden:
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.
Bullshit.
Cheers,
- Alf
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