# Re: differences heard between random high frequency sound and sinusoids

```Thank you Willem and Axel for your answers,

Using signal of substential duration, the answer is clear, there is a
difference.
For shorter windows (let's say 1 second and shorter), it seems the
question is more difficult to answer.
I just thought also about the Fourier serie which actually provides a
set of stationary sinusoids which can represent perfecting a limited
band of noise in a short window.
The general case being to complex to handle here. I'll just go right
to the context of my question:

In speech processing, we often use deterministic + noise models.
The deterministic component find a motivation in the representation of
the periodic glottal pulses.
For the noise component, two motivations can exist:
1) The noise represents the aspiration noise (produced also at the
level of the glottis).
or/and
2) Whereas a clear harmonic grid usually appears for voiced sounds at
low frequencies, the high frequency content of a spectrogram is
blurred. Consequently, a noise component seems a convenient
representation of this part of the spectrum where sinusoids would be
difficult to track. And (here is the reason of my question), this
motivation is even stronger if we do not perceive differences between
noise and whatever could be the underlying signal (e.g. highly
frequency modulated harmonics).

Therefore, the class of sinusoids which is here considered is:
harmonic and non-stationary.
Any idea/reference for this precise context is welcome (Thanks Axel
and Willem for the references you already sent me !)

Bests,
Gilles

On Fri, Jul 20, 2012 at 3:36 AM, Axel Roebel <Axel.Roebel@xxxxxxxx> wrote:
> Hello Gilles, hello Willem
>
> On 20/07/2012 00:26, Willem Christiaan Heerens wrote:
>> Dear Gilles,
>>
>>
>> There is a very simple answer to your question about the statement:
>>
>> At high frequencies, it is "often said" that we do not perceive differences
>> between random and deterministic components.
>>
>> That answer is:
>>
>> No this statement is erroneous. We definitely hear great differences. They
>> depend on the ‘composition’ of the contributing sinusoids. But also on the
>> length of the period of listening.
>>
>
> I certainly agree on the last 2 phrases of this paragraph of the answer.
>
> For the rest I wonder whether the simple answer (even if technically
> perfectly correct) is not a bit too much biased to a very small (and for
> natural sounds, like speech and music) rather irrelevant class of
> "deterministic components" that are stationary sinusoids?
>
> I would think that the experiments about the relation between density
> of deterministic components that are required to be perceptually
> equivalent to noise that are described here
>
> http://mediatheque.ircam.fr/articles/textes/Gerzso80a/
>
> could be interesting for Gilles. For low frequencies the authors found
> that the number of sinusoids (with a certain frequency distribution)
> that is required to create a perception of noise is constant for
> critical bands. For higher bands this number seems to increase.
> Unfortunately experiments stop at 4500Hz, in extrapolating to higher
> frequencies the authors suggest that one needs more sinusoids per
> critical band  in high frequencies than in low frequencies to simulate
> band limited noise. The report states that subjects used roughness and
> regularity as cues (that's well in line with answer below because the
> suggested signals are perfectly regular and therefore easily
> distinguished from noise )
>
> Here another paper by P Hanna that touches the area but does not provide
> any perceptual tests
>
>
> As far as I saw these experiments deal all with stationary sinusoids,
> and therefore may not be so relevant for the perception of natural
> sounds (speech), for which - as long as one accepts the sinusoidal model
> - sinusoidal amplitudes and frequencies should change over time.
>
> I am not aware of other experiments in that direction but would find it
> interesting to read about them as we are currently doing research
> on a related question.
>
> Best
> Axel
>
>> And in such compositions both the choices of frequencies and phases have
>> strong influence.
>>
>> For example:
>>
>> Please calculate with high resolution the following three compositions,
>> using five sinusoids:
>>
>> 1.    10,000 / 10,002 / 10,004 / 10,006 / 10,008 Hz. All sine
>> contributions.
>>
>> In that case you will hear the high tone that corresponds with 10,004 Hz but
>> with a strong beat of 2 Hz.
>>
>> 2.    10,000 / 10,004 / 10,008  Hz. All three sine contributions.
>> 10,002 / 10,006 Hz.  Both cosine contributions. So a 90 degree phase shift.
>>
>> In that case you will hear the high tone that corresponds again with 10,004
>> Hz but now with a strong 4 Hz beat.
>>
>> 3.    10,000 / 10,002.0333 / 10,004 / 10,006.0333 / 10,008 Hz. All sine
>> contributions.
>>
>> In that case you will hear the high tone of 10,004 Hz again, but within a
>> period of 30 seconds and starting with a 2 Hz beat after 7.5 seconds the
>> beat will gradually change into a 4 Hz beat. After 15 seconds the beat is
>> back again at 2 Hz. At 22.5 seconds again at 4 Hz and after 30 seconds the
>> composition ends with a 2 Hz beat in the 10,004 Hz tone.
>>
>> If you change the sine contributions of 10,002.0333 and 10,006.0333 Hz into
>> cosine the composition starts with a beat of 4 Hz, 2 Hz at 7.5 sec, 4 Hz at
>> 15 sec, 2 Hz at 22.5 sec and finally 4 Hz at 30 sec.
>>
>> For noise filtered by a narrow band-pass around 10 kHz it is known that we
>> will hear just a 10 kHz tone. Nothing more.
>>
>> So on your question:
>>
>> For example, do we perceive a difference between a few sinusoids around
>> 10kHz and a band-pass filtered noise around the same frequency?
>>
>> The answer is clear:  Although, according to existing perception theory, the
>> different frequency contributions in the composition are entirely unresolved
>> we can hear differences related to different phase and frequency settings.
>>
>> And at your request:
>>
>> Anybody have some references or links for this subject ?
>>
>> What do you think about my reply? Does it fulfill your request?
>>
>> In this context I also want to repeat August Seebeck’s statement that he
>> published in the year 1844:
>>
>> “How else can the question as to what makes out a tone be decided but by the
>> ear?”
>>
>> It was part of his answer to the erroneous hypotheses of Ohm about pitch
>> perception in the famous Ohm-Seebeck dispute.
>>
>> And I want to add the following to it:
>>
>> The above described sound experiments with indisputable results are entirely
>> based on the hearing theory I have described together with J. A. de Ru in
>> the booklet:
>>
>> Applying Physics Makes Auditory Sense
>>
>> Based on the concept in this booklet that our hearing sense is
>> differentiating and squaring the incoming sound pressure stimulus, this
>> mechanism evokes in front of the basilar membrane the sound energy frequency
>> spectrum.
>>
>> In that case Fourier series calculations show exactly the frequency spectrum
>> including the 2, 4, 6 and 8 Hz difference frequency contributions. Of which
>> the 2 and 4 Hz frequencies are responsible for the beat phenomena.
>>
>> If you are interested in further detail please contact me.
>>
>>
>> Kind regards
>>
>>
>> Willem C. Heerens
>>
>>
>>
>> On Thu, 19 Jul 2012 19:08:30 +0300, Gilles Degottex
>> <gilles.degottex@xxxxxxxx> wrote:
>>
>>> Hi all,
>>>
>>> At high frequencies, it is "often said" that we do not perceive
>>> differences between random and deterministic components.
>>> For example, do we perceive a difference between a few sinusoids
>>> around 10kHz and a band-pass filtered noise around the same frequency
>>> ?
>>> Anybody have some references or links for this subject ?
>>>
>>> Bests,
>>> Gilles
>>> --
>>> ICS - FORTH
>>> Vasilika Vouton, P.O. Box 1385
>>> GR 71110 Heraklion, Crete, Greece
>>> Mobile: +30 6942 207403
>>> Work:   +30 2810 391580
>>
>
>
> --
> Axel Roebel
> Head of the Analysis/Synthesis Team, IRCAM
> Phone: ++33-1-4478 4845 | Fax: ++33-1-4478 1540

--
ICS - FORTH
Vasilika Vouton, P.O. Box 1385
GR 71110 Heraklion, Crete, Greece
Mobile: +30 6942 207403
Work:   +30 2810 391580

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