# Re: Discontinuities in stimulus. (Fred Herzfeld )

```Subject: Re: Discontinuities in stimulus.
From:    Fred Herzfeld  <herzfeld@xxxxxxxx>
Date:    Fri, 17 Oct 2008 15:44:24 -0400
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Hello Ranjit,

Consider the Fourier Transform of a signal consisting of a single sinusoid. Then the amplitude is
say A and the phase is phi. Now delete a small section delta from the wave form at the peak of the
sinusoid.  Each of the FT integrals is reduced by the product of the time delta and the particular
basis. Now repeat the same gedanken experiment but with the delta placed at the point when the
signal sinusoid is near zero. It is then obvious that there will be differences in the FT and
therefore what the ear hears. It should also be obvious now that if the signal frequency and the
time at which the delta section is deleted are not commensurate the differences outlined above will
continue to drift from the peak to the valley and thus generate "fluttering".

The answer to the second part of your question is in general "it cannot be done". However if you
know for example that the stimulus consists of a known number of harmonics of a known fundamental
frequency or at least a known number of specified frequencies and their amplitudes and phases then
the problem of the determination if "outages" exist is in theory solvable. Not necessarily easy

Fred
------------------------------
Ranjit Randhawa wrote:
> Dear List,
> I have a rather simple question concerning the usual assumption made
> about the need for "continuity" of a stimulus. My interest arose when I
> started exploring the "fluttering" sound heard for some stimuli. A
> simple way to create a stimulus to study this phenomenon was to insert
> periodic "discontinuities" in a pure sinusoid of low frequency by simply
> deleting bits from this stimulus in a consistent manner. My next step
> was to try and create a model, which became problematic as the resultant
> sound heard was dependent both on the size of the deleted section and
> also on where the deletion was performed. Does anyone have an easy
> method for determining first, that a discontinuity in the stimulus has
> occurred and second and more importantly, where.
> Thanks in advance for any insights,
> Randy Randhawa
>
>

--
Fred Herzfeld, MIT '54
78 Glynn Marsh Drive #59
Brunswick, Ga.31525
USA
```

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