Alf P. Steinbach wrote:
> * Steve Holden:
>> Alf P. Steinbach wrote:
>>> * Grant Edwards:
>>>> On 2010-01-15, Steve Holden <st...@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.
>>>
>> Though for what it's worth I wasn't impressed by the results of running
>> the posted program, since it yielded an AIFF file of mostly zeroes that
>> produced no audible sound.
>>
>> $ od -bc sinewave.aiff
>> 0000000 106 117 122 115 000 002 261 076 101 111 106 106 103 117 115 115
>> F O R M \0 002 261 > A I F F C O M M
>> 0000020 000 000 000 022 000 001 000 001 130 210 000 020 100 016 254 104
>> \0 \0 \0 022 \0 001 \0 001 X 210 \0 020 @ 016 254 D
>> 0000040 000 000 000 000 000 000 123 123 116 104 000 002 261 030 000 000
>> \0 \0 \0 \0 \0 \0 S S N D \0 002 261 030 \0 \0
>> 0000060 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
>> \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0 \0
>> *
>> 0530500 000 000 000 000 000 000
>> \0 \0 \0 \0 \0 \0
>> 0530506
>>
>> Any idea what I did wrong?
>
> That sounds like something I did wrong, not like something you did wrong:
>
> It sounds like a ... BUG! ... in my simple_writer code. :-)
>
> Or, that's perhaps not funny, but it occurred to me that it might, to
> some at least, appear to be sort of incongruous in the context of the
> earlier thread. Heh.
>
> Checking first 20 sample values generated:
>
> <code>
> if True:
> f = 440
> sample_rate = 44100
> total_time = 2
> n_samples = sample_rate*total_time
>
> writer = simple_sound.Writer( "sinewave.aiff" )
> for i in range( n_samples ):
> t = 1*i/sample_rate
> sample = sample_squares( f, t )
> if i < 20: print( sample ) # Check 'em
> writer.write( sample )
> writer.close()
> </code>
>
> <output>
> -0.0314107590781
> -0.0314107590781
> -0.0941083133185
> -0.15643446504
> -0.218143241397
> -0.278991106039
> -0.338737920245
> -0.397147890635
> -0.45399049974
> -0.50904141575
> -0.562083377852
> -0.612907053653
> -0.661311865324
> -0.707106781187
> -0.75011106963
> -0.790155012376
> -0.827080574275
> -0.860742027004
> -0.891006524188
> -0.917754625684
> </output>
>
> Checking generated file:
>
> <dump>
> $ od -bc sinewave.aiff | head
> 0000000 106 117 122 115 000 001 130 266 101 111 106 106 103 117 115 115
> F O R M \0 001 X 266 A I F F C O M M
> 0000020 000 000 000 022 000 001 000 000 254 104 000 020 100 016 254 104
> \0 \0 \0 022 \0 001 \0 \0 254 D \0 020 @ 016 254 D
> 0000040 000 000 000 000 000 000 123 123 116 104 000 001 130 220 000 000
> \0 \0 \0 \0 \0 \0 S S N D \0 001 X 220 \0 \0
> 0000060 000 000 000 000 000 000 373 373 373 373 363 364 353 372 344 024
> \0 \0 \0 \0 \0 \0 373 373 373 373 363 364 353 372 344 024
> 0000100 334 112 324 245 315 053 305 344 276 330 270 016 261 215 253 133
> 334 J 324 245 315 + 305 344 276 330 270 016 261 215 253 [
> </dump>
>
>
> Hm, I'm inclined to think that you used Python 2.x instead of my 3.1.1!
>
> I no longer have Python 2.x installed, I think, so no time to test that
> now.
>
> But would that be the case?
>
> If so, perhaps changing "t = 1*i/sample_rate" to "t =
> (1.0*i)/sample_rate" will help?
>
>
> Cheers,
>
> - Alf
That was indeed the case. So here you have an interesting example of a
piece of code that is pathological in Python2. All you have to change is
to add
from __future__ import __division__
and bingo! It's a multi-language program. But try seeing what 2to3 says
about your Python3 code :)
I will forgive you the omission of the ".0" because I too would assume
that it would be slower. Of course another technique is to scale the
already floating-point raw values before dividing by the range of the
analog output - then an integer division should work basically fine?
Under Python 3 I see
0000000 106 117 122 115 000 002 261 076 101 111 106 106 103 117 115 115
F O R M \0 002 261 > A I F F C O M M
0000020 000 000 000 022 000 001 000 001 130 210 000 020 100 016 254 104
\0 \0 \0 022 \0 001 \0 001 X 210 \0 020 @ 016 254 D
0000040 000 000 000 000 000 000 123 123 116 104 000 002 261 030 000 000
\0 \0 \0 \0 \0 \0 S S N D \0 002 261 030 \0 \0
0000060 000 000 000 000 000 000 373 373 373 373 363 364 353 372 344 024
\0 \0 \0 \0 \0 \0 373 373 373 373 363 364 353 372 344 024
0000100 334 112 324 245 315 053 305 344 276 330 270 016 261 215 253 133
334 J 324 245 315 + 305 344 276 330 270 016 261 215 253 [
0000120 245 176 237 375 232 335 226 043 221 324 215 364 212 210 207 222
245 ~ 237 375 232 335 226 # 221 324 215 364 212 210 207 222
0000140 205 026 203 026 201 224 200 222 200 021 200 021 200 222 201 224
205 026 203 026 201 224 200 222 200 021 200 021 200 222 201 224
0000160 203 026 205 026 207 222 212 210 215 364 221 324 226 043 232 335
203 026 205 026 207 222 212 210 215 364 221 324 226 # 232 335
0000200 237 375 245 176 253 133 261 215 270 016 276 330 305 344 315 053
237 375 245 ~ 253 [ 261 215 270 016 276 330 305 344 315 +
0000220 324 245 334 112 344 024 353 372 363 364 373 373 004 005 014 014
324 245 334 J 344 024 353 372 363 364 373 373 004 005 \f \f
and so on, but I still get silence from the Quicktime player.
regards
Steve
--
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