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Re: Gaussian vs uniform noise audibility

Dear List:

To resolve the Gaussian vs. uniform audibility issue for
myself, I conducted a comparison test.  I created
alternating bursts of each noise type and summed them
together.  If the levels of each could be adjusted such
that I could not detect any alternations, I concluded
that there was no audible difference.

The bursts consisted of 0.125 second rising and 0.125
second falling phases, with no sustained full-on or
full-off phases.  The rising phase of one source
intersected the falling phase of the other where each was
at its -3 dB point.  Cos^0.5 (square root) rise/fall
shapes insured that the two sources always summed to a
constant RMS level.  Base levels were set to insure that
clipping could not occur on instantaneous peaks.

I tested Gaussian white noise with standard deviations of
2.0, 1.0, 0.5, and 0.1, compared to uniform white noise.
Noise sources were continuous and non-repeating.  I found
that in all cases except for SD = 0.1 the levels could
be adjusted to give the percept of a single continuous

Since Gaussian noise has much higher peak-to-average
ratios than uniform noise, the level adjustments
consisted of reductions in the uniform noise level to get
a match.  For the standard deviations used, the relative
reductions were 1.5, 4.5, 10.5, and 21.5 dB, respectively.

The SD = 0.1 case was clearly different, as could be
told immediately when switched to continuous non-burst
operation.  Not only was there a conspicuous audible
difference, the waveforms showed a conspicuous visible
difference as well, which pointed toward the explanation:

With low-SD noise, there is a large peak-to-average
ratio.  The peak values come relatively infrequently,
and when they do they create spectral splatters during
the relatively short auditory temporal integration time,
even though the Gaussian source still has a flat spectrum
if averaged long enough.  It is the spectral splatters
that are making the audible difference.

At higher SD the average level is also higher, and the
peaks and consequent splatters are more frequent as well,
so the splatters are masked as well as integrated.

I ran these tests with my DaqGen for Windows (shameless
plug), which I modified especially for this purpose by
the addition of half-power cosine window steps.  Since
I was about to release version 1.10 anyway, I included
that feature and an application note, along with a
sound setup file to duplicate the above tests.  You
are welcome to download this and try it for yourself.
(DaqGen is freeware, so there are no obligations.)

To run the test, start DaqGen and hit Load Setup
(either in the File menu or the the button near the
bottom right of the Generator dialog).  Select
the GausWhit.GEN setup from the pop-up dialog.
You will need to adjust your mixer settings for a
comfortable listening level, either from the
normal Windows mixer or the dialog that pops
up when you hit the Vol button in the Generator

To read more about this, including a recap of
the discussion above, open the DaqGen Help system
and go to Application Notes in the Contents,
then select the topic entitled "GausWhit.GEN Setup File -
Comparing Noise Distributions".

I'll be glad to answer any questions.


Robert Masta

         D A Q A R T A
Data AcQuisition And Real-Time Analysis
 Shareware from Interstellar Research