A simple-to-use sound file writer

[Grant Edwards]

On 2010-01-14, Alf P. Steinbach <alfps at start.no> wrote:

>> It's not clear to me that you can approximate any waveform
>> with a suitable combination of square waves,
>
> Oh. It's simple to prove. At least conceptually! :-)

[...]

> 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 voil?, 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!

Huh?  I've only studied basic DSP, but I've never heard/seen
that as the basis of digital represention of sound.  I've also
never seen that representation used anywhere.  Can you provide
any references?

-- 
Grant Edwards                   grante             Yow! CHUBBY CHECKER just
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