A simple-to-use sound file writer
Alf P. Steinbach
alfps at start.no
Sat Jan 16 07:26:08 CET 2010
* Grant Edwards:
> On 2010-01-15, Steve Holden <steve at holdenweb.com> wrote:
>
>> I will, however, observe that your definition of a square wave is what I
>> would have to call a "'square' wave" (and would prefer to call a "pulse
>> train"), as I envisage a square wave as a waveform having a 50% duty
>> cycle, as in
>>
>> ___ ___
>> | | | |
>> | | | |
>> | | | |
>> +---+---+---+---+ and so on ad infinitum, (though I might allow you
>> | | | | to adjust the position
>> | | | | of y=0 if you want)
>> |___| |___|
>
> That is a square wave.
>
>> as opposed to your
>>
>> _
>> | |
>> | |
>> ______| |______ ______
>> | |
>> | |
>> |_|
>
> That isn't.
>
> Arguing to the contrary is just being Humpty Dumpty...
Neither I nor Steve has called that latter wave a square wave.
Steve, quoted above, has written that I defined a square wave that way. I have
not. So Steve's statement is a misrepresentation (I described it as a sum of two
square waves, which it is), whatever the reason for that misrepresentation.
>> Or, best of all, you could show me how to synthesize any
>> waveform by adding square waves with a 50% duty cycle. Then I
>> *will* be impressed.
>
> Isn't that what he claimed? He said that his algorithm for
> summing square waves demonstrated the converse of the ability
> to construct a periodic function (like a square wave) from a
> sine-cosine summation.
Not by itself, no: it just synthesizes a sine.
For the more general case read e.g. the PS in my reply to your earlier (single)
article in this thread.
For information about what the algorithm does, what you refer to as a "claim"
(but note that a Python implementation has been posted to this thread, and that
it works, and that besides the algorithm is trivial so that "claim" is a rather
meaningless word here), read the article that you then responded to.
Cheers & hth.,
- Alf
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