Carlos Moreno wrote:

...

> The period is 4 samples.  It looks more or less like the following:
> 
>   o               o
>   |               |
>   |               |
>   |               |
> --+---o---+---o---+---o---+---o--- ....
>           |               |
>           |               |
>           |               |
>           o               o
> 
> 
> If all the non-zero samples had the same magnitude, then the above
> would exactly represent a sinusoid with frequency = Fs/4 (angular
> frequency pi/2)
> 
> But then, the bottom samples are not equal to -7FFF, but -7FFF - 1
> 
> So, the resulting signal is a perfect sinusoid at Fs/4, plus a
> signal that consists of one sample with value -1 every four samples
> (ok, I said +1 every four samples -- is that the detail you're
> picking on? -- it would be +1 if we look at the sinusoid being
> +8000 and -8000 -- assuming that there wasn't integer overflow
> in such case -- but yes, it makes more sense to think of +7FFF
> and -7FFF, which is the only way that it could fit in the binary
> representation).
 >
> That involves a DC component of -0.25, plus spectral content at
> Fs/4 (because this is the fundamental period of the "added"
> signal), with harmonics at Fs/2.
> 
> Notice that the detail you mention ("the pair occurs twice")
> is not correct;  the second occurence belongs in the next
> period of the signal;  it occurs once per period, or once
> every four samples.

I was wrong on two counts. There are no added harmonics at all, only an 
offset. The pattern isn't repeated twice (why on earth did I think so?) 
so the DC bin is simply $7FFF + $8000 - -1.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:

> P.S. Do you now see that [1 1 0 -1 -1 0] is sinusoidal at Fs/6? 

Oh, yes -- I see it now, and I always saw it;  my comment in your
original post about this was that if we are trying to make the
ear hurt, we might as well go for the "ultimate pain" that would
cause the sequence [1 1 -1 -1]  :-)

> It has 
> no even harmonics or harmonics divisible by 3, so the lowest harmonic is 
> 5Fs/6, and that is 14 dB down. It is the so-called "modified sine wave" 
> of uninterruptible power supplies.

Ok, no, this part, I hadn't thought about  :-)

I always thought the UPS generation was based on approximating
a sine wave with a width-modulated pulses that was naturally
LP-filtered by the transformer.  I guess the above sequence
*is* LP-filtered by the transformer (otherwise the power-amp
required to handle the analog output signal would be too
expensive) -- aren't there any unwanted effects from the sinc
spectral envelope involved in the reconstruction filter when
each sample is output as a constant signal during the entire
sampling period?  (subject for a whole new thread, maybe?)

Carlos
--

Jerry Avins wrote:
> Carlos Moreno wrote:
> 
>> Al Clark wrote:
>>
>>>> There's no need to get into that. The generated second harmonic will 
>>>> be 96 dB down from the fundamental. Masking will surely make it 
>>>> inaudible even in the absence of a reconstruction filter (which 
>>>> should remove 
>>>
>>>
>>>
>>> Yeh, and it will be at DC and PI (fs/2). 
>>
>>
>>
>> No -- it's one added 1 every four samples -- that's fs/4, with DC
>> and harmonic content at fs/2
> 
> 
> What's with you in this thread? There is DC because $7FFF +$8000  = -1 
> and the pair occurs twice to give a DC of -2. 

Let's revisit the original C code with the glitch detected by Randy:

>>for(k = 0;k < N/4;k++) {
>>>    sound[4*k] = 0x7FFF;
>>>    sound[4*k+1] = 0;
>>>    sound[4*k+2] = 0x8000;
>>>    sound[4*k+3] = 0;
>>> }
> 
> 
> 1. Not a sine. Try 0x8001 instead of 0x8000.  ;) 

The period is 4 samples.  It looks more or less like the following:

   o               o
   |               |
   |               |
   |               |
--+---o---+---o---+---o---+---o--- ....
           |               |
           |               |
           |               |
           o               o


If all the non-zero samples had the same magnitude, then the above
would exactly represent a sinusoid with frequency = Fs/4 (angular
frequency pi/2)

But then, the bottom samples are not equal to -7FFF, but -7FFF - 1

So, the resulting signal is a perfect sinusoid at Fs/4, plus a
signal that consists of one sample with value -1 every four samples
(ok, I said +1 every four samples -- is that the detail you're
picking on? -- it would be +1 if we look at the sinusoid being
+8000 and -8000 -- assuming that there wasn't integer overflow
in such case -- but yes, it makes more sense to think of +7FFF
and -7FFF, which is the only way that it could fit in the binary
representation).

That involves a DC component of -0.25, plus spectral content at
Fs/4 (because this is the fundamental period of the "added"
signal), with harmonics at Fs/2.

Notice that the detail you mention ("the pair occurs twice")
is not correct;  the second occurence belongs in the next
period of the signal;  it occurs once per period, or once
every four samples.

Carlos
--

Carlos Moreno wrote:

   ...

> Well, again, this goes exactly with what I was saying -- when
> saying that who would distinguish the two versions, someone
> claim (well, implied) that a dog would.  There's plenty of
> reasons why neither a dog nor a human would be able to
> distinguish them -- my point was that if anything, the
> argument would have to be in reverse:  if *one* of them were
> able to, it would be the human ear.

This started out about dogs being able ho hear much higher frequencies 
that humans. Google "dog whistle".

> Why would it remove it?  If it is part of the samples, the it
> is part of the signal that would be reconstructed.  It's a
> perfect sine wave added to a signal that consists of a sample
> with value 1 every four samples.  Why would that be eliminated
> by the reconstruction filter?

A brainfart. I was thinking Fs/2 for the fundamental and Fs for the 
harmonic. In fact, the frequencies are half those.

Jerry

P.S. Do you now see that [1 1 0 -1 -1 0] is sinusoidal at Fs/6? It has 
no even harmonics or harmonics divisible by 3, so the lowest harmonic is 
5Fs/6, and that is 14 dB down. It is the so-called "modified sine wave" 
of uninterruptible power supplies.
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

thanks a lor krishna for your valuable advice eill try to get the book
and read it.
also when i say sine wave it should o/p sine wave from any of the
computer ports

Carlos Moreno wrote:
> Al Clark wrote:
> 
>>> There's no need to get into that. The generated second harmonic will 
>>> be 96 dB down from the fundamental. Masking will surely make it 
>>> inaudible even in the absence of a reconstruction filter (which 
>>> should remove 
>>
>>
>> Yeh, and it will be at DC and PI (fs/2). 
> 
> 
> No -- it's one added 1 every four samples -- that's fs/4, with DC
> and harmonic content at fs/2

What's with you in this thread? There is DC because $7FFF +$8000  = -1 
and the pair occurs twice to give a DC of -2. the waveform consists of 
an offset of 2, a fundamental of $7FFF.8 at Fs/4, and a second harmonic 
$-0.8 at Fs/2. On the positive peaks $7FFF.8 and $-.8 add to $7FFF. On 
the negative peaks, $-7FFF.8 and $-.8 add to $8000 (IOW, $-8000). (Note 
that the harmonic changes sign twice when the fundamental changes once.)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Al Clark wrote:

>>There's no need to get into that. The generated second harmonic will be 
>>96 dB down from the fundamental. Masking will surely make it inaudible 
>>even in the absence of a reconstruction filter (which should remove 
> 
> Yeh, and it will be at DC and PI (fs/2). 

No -- it's one added 1 every four samples -- that's fs/4, with DC
and harmonic content at fs/2

Carlos
--

Jerry Avins wrote:
> Carlos Moreno wrote:
> 
>> Al Clark wrote:
>>
>>>>>> Yeah, but what about my dog...
>>>>
>>>>
>>>>
>>>> Your dog??  Your dog is far (faaaaaaaar) less capable than you
>>>> to *distinguish* the two versions.  Probably wouldn't even
>>>> distinguish two things with frequencies 10% apart -- which is
>>>> a much much much more severe difference than the tiny 1-bit of
>>>> noise that Randy caught (on the screen -- no way he would have
>>>> caught it coming from a speaker or headphones!  ;-))
>>>
>>>
>>>
>>> The 0x8000 is going to cause even order harmonic distortion. Its not 
>>> going to impact the frequency (fs/4).
>>
>>
>>
>> This is exactly what I was saying.
>>
>> My point was precisely, a dog would be utterly incapable of
>> distinguishing both versions -- from what I've read, the dog's
>> ear is actually far less capable than the human in terms of
>> *distinguishing* sounds with slightly different characteristics
>> (even if it was a frequency change that for us, humans, was
>> extremely obvious)
> 
> 
> There's no need to get into that. The generated second harmonic will be 
> 96 dB down from the fundamental. 

Well, again, this goes exactly with what I was saying -- when
saying that who would distinguish the two versions, someone
claim (well, implied) that a dog would.  There's plenty of
reasons why neither a dog nor a human would be able to
distinguish them -- my point was that if anything, the
argument would have to be in reverse:  if *one* of them were
able to, it would be the human ear.

> Masking will surely make it inaudible 
> even in the absence of a reconstruction filter (which should remove it).

Why would it remove it?  If it is part of the samples, the it
is part of the signal that would be reconstructed.  It's a
perfect sine wave added to a signal that consists of a sample
with value 1 every four samples.  Why would that be eliminated
by the reconstruction filter?

Carlos
--

Jerry Avins <jya@ieee.org> wrote in news:5fGdndU-
GtXu6aPZnZ2dneKdnZydnZ2d@rcn.net:

> Carlos Moreno wrote:
>> Al Clark wrote:
>> 
>>>>>> Yeah, but what about my dog...
>>>>
>>>>
>>>> Your dog??  Your dog is far (faaaaaaaar) less capable than you
>>>> to *distinguish* the two versions.  Probably wouldn't even
>>>> distinguish two things with frequencies 10% apart -- which is
>>>> a much much much more severe difference than the tiny 1-bit of
>>>> noise that Randy caught (on the screen -- no way he would have
>>>> caught it coming from a speaker or headphones!  ;-))
>>>
>>>
>>> The 0x8000 is going to cause even order harmonic distortion. Its not 
>>> going to impact the frequency (fs/4).
>> 
>> 
>> This is exactly what I was saying.
>> 
>> My point was precisely, a dog would be utterly incapable of
>> distinguishing both versions -- from what I've read, the dog's
>> ear is actually far less capable than the human in terms of
>> *distinguishing* sounds with slightly different characteristics
>> (even if it was a frequency change that for us, humans, was
>> extremely obvious)
> 
> There's no need to get into that. The generated second harmonic will be 
> 96 dB down from the fundamental. Masking will surely make it inaudible 
> even in the absence of a reconstruction filter (which should remove 
it).
> 
> Jerry

Yeh, and it will be at DC and PI (fs/2). 

-- 
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com

Carlos Moreno wrote:
> Al Clark wrote:
> 
>>>>> Yeah, but what about my dog...
>>>
>>>
>>> Your dog??  Your dog is far (faaaaaaaar) less capable than you
>>> to *distinguish* the two versions.  Probably wouldn't even
>>> distinguish two things with frequencies 10% apart -- which is
>>> a much much much more severe difference than the tiny 1-bit of
>>> noise that Randy caught (on the screen -- no way he would have
>>> caught it coming from a speaker or headphones!  ;-))
>>
>>
>> The 0x8000 is going to cause even order harmonic distortion. Its not 
>> going to impact the frequency (fs/4).
> 
> 
> This is exactly what I was saying.
> 
> My point was precisely, a dog would be utterly incapable of
> distinguishing both versions -- from what I've read, the dog's
> ear is actually far less capable than the human in terms of
> *distinguishing* sounds with slightly different characteristics
> (even if it was a frequency change that for us, humans, was
> extremely obvious)

There's no need to get into that. The generated second harmonic will be 
96 dB down from the fundamental. Masking will surely make it inaudible 
even in the absence of a reconstruction filter (which should remove it).

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������