A simple-to-use sound file writer
Alf P. Steinbach
alfps at start.no
Thu Jan 14 11:14:24 EST 2010
* Mel:
> Alf P. Steinbach wrote:
>> * Steve Holden:
>
>>> 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! :-)
>>
>> Consider first that you need an infinite number of sine waves to create a
>> perfect square wave.
>>
>> The opposite also holds: infinite number of square waves to create a
>> perfect sine wave (in a way sines and squares are opposites, the most
>> incompatible).
>
> No, it doesn't. The infinite set of sine waves that make a square wave
> leave out the sine waves of frequency 2f, 4f, 6f, 8f, ... (2*n*f) ... .
> Once you've left them out, you can never get them back. So sawtooth waves,
> for example, can't generally be built out of sets of square waves.
The way to build a sine wave out of square waves is not a Fourier transform.
See the post you replied to for a simple procedure to build the sine wave.
Cheers & hth.,
- Alf
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