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18th February 2015, 06:14 PM  #1 
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Join Date: Apr 2014
Location: Italy friuli

Shannon ad fc/2 tricks
Hi guys , reading the Shannon theorem i have found a trick
Is quiet that theorem tell the maximum frequencies for your signal from analog to digital becomes a maximum value of fc/2 where fc is a sample rate . But if you have a pure sine tone at frequencies 15khz and using acquisition asynchronous Samples describing a 2 other tones at low frequencies generated from data output of dac the calculus is sin(2*3.14159*15000*kt) and for example t = 1/44100 if iu put this under a spreadsheet and print result of ideal smple rate you can see the envelope the problem start about at fc/9 and have minimums at fc/3 and fc/9 . Nearest this values the acquisition create a sine frequncies modulation . I think the problem is the sinc on atempt of recostruction of signal next post the immages of results 
18th February 2015, 06:42 PM  #2 
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Join Date: Apr 2014
Location: Italy friuli

Results of smples
this is an image of samples
the 2 tones of modulation have no the same phase 
18th February 2015, 06:54 PM  #3 
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Join Date: Apr 2014
Location: Italy friuli

About fc/6
Nearest Fc/6 another trick sine have 7500hz .
If the sinc on the conversion DA is not assailable to an impulse the result is another modulation in the end the samples lost the phase information Last edited by gumo73; 18th February 2015 at 06:56 PM. 
18th February 2015, 07:24 PM  #4 
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Join Date: Apr 2014
Location: Italy friuli

nearest fc/9
In this case the values have a small modulation
fo = 5600hz . This is my examples . I think the same problem becomes with digital filters wit high fault rates 
18th February 2015, 07:31 PM  #5 
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Join Date: Apr 2014
Location: Italy friuli

The vinyl
I think in the end we need the vinyl for Hiend audio chains

18th February 2015, 08:20 PM  #6 
diyAudio Member
Join Date: May 2007

You need to find out what a reconstruction filter does. Then you will understand why hiend audio chains can be built without vinyl.

18th February 2015, 08:37 PM  #7 
diyAudio Member

This isn't a digital problem, if you combine two tones and cut them into vinyl, you'll see the same "envelope" effect on playback.

19th February 2015, 10:13 AM  #8 
diyAudio Member
Join Date: May 2007

The OP is seeing ultrasonic images, which the reconstruction filter will remove. These images, if left unfiltered, will cause beats with the wanted sound as he shows in his plots. It is quite common for people who don't understand digital audio to frighten themselves in this way.

19th February 2015, 12:13 PM  #9  
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Quote:
__________________
"The question of who is right and who is wrong has seemed to me always too small to be worth a moment's thought, while the question of what is right and what is wrong has seemed allimportant." Last edited by scott wurcer; 19th February 2015 at 12:18 PM. 

19th February 2015, 01:20 PM  #10 
diyAudio Member
Join Date: Apr 2014
Location: Italy friuli

simulation
There is no combination about any 2 tones .
the result is ideal ADC by a sheet or on matlab or on octave or others mathematical programs The print is only samples without no interpolation the calculus is sin( 2*3.14159*fo*kt) where kt is the time of samples k= 1,2,3,,.....,n or k=,numberstart,+1,+2,+3,+4,+n,numberend , t=1/44100Hz , fo=15000Hz Printed are the result . On sheet by example k=12 t=1/44100Hz  k  Amplitude   12  =sin( 2*3.14159*15000*12* 2.2676e05)  13  =sin( 2*3.14159*15000*13* 2.2676e05)  14  =sin( 2*3.14159*15000*14* 2.2676e05) .........  n  =sin( 2*3.14159*15000*n* 2.2676e05) a variation you can put a delay Last edited by gumo73; 19th February 2015 at 01:31 PM. 
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