Re: Granular synthesis and auditory segmentation

[Jont Allen <jba@xxxxxxxxxxxxxxxx>]

meijer@NATLAB.RESEARCH.PHILIPS.COM wrote:
>
> Jont Allen asked
>
> > Are two tones that beat stationary or non-stationary,
> > by your definition?
>
> Stationary. The frequency content is the same at all times
> in your example. This is how stationary is defined in signal
> theory.
>

What about three tones, making up an amplitude modulated carrier,
with a 0.01 Hz 100% modulation. Is that also stationary?
It has three continuous tones. Thus by your definition, it is.
Yet there are long streches where there is no signal.

Is a periodic gated tone burst stationary?
The tone is on for 100 ms and off for 100 ms.

If you say it is nonstationary, then I will say that
I can do a fourier analysis of this stimulus in terms of sinewaves,
if I use an analysis interval of 200 ms. Thus by your definition
it would be stationary. Yet the ear would hear a click as the
tone burst turned on.

My conclusion is that when you deal with filterbanks (as in the ear),
the term stationary must be applied only in the ensemble sense.

As I see it "stationary" depends on the time scale, which is
another way of saying the same thing.

Jont

--
Jont B. Allen, Room E161
AT&T Labs-Research, Shannon Laboratory
180 Park Ave.
Florham Park NJ 07932-0971
973/360-8545voice, x7111fax, http://www.research.att.com/info/jba
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