A simple-to-use sound file writer

[Alf P. Steinbach]

* 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.

Oh, you have... The end result above (for finite n) is a sequence of sample 
values of a sine wave. Ordinary digital representation of sound is exactly the 
same, a sequence of sample values.


> I've also never seen that representation used anywhere.

Yes, you have. A sequence of sample values is the representation used in any 
direct wave file. Like [.wav]  and, I believe, [.aiff].


>  Can you provide any references?

I don't have any references for the above procedure, it's sort of trivial. 
Probably could find some references with an hour of googling. But no point.


Cheers & hth.,

- Alf


PS: To extend the above to a non-symmetric waveform, just first decompose that 
waveform into sine waves (Fourier transform), then add up the square wave 
representations of each sine wave. :-)