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Many thanks !!

Dear all who replied,

All your mails are very helpful. Thanks a great lot !

I pasted all the replies below (I hope I didn't forget any).


Here's what I got concerning equivalent square noise:

Fred Wightman wrote :

The equivalent square bandwidth is simply the width of a rectangle
that has the same total area (noise power) and the same height as
your noise spectrum. So, to get the width, first get the total
"power". Let's say it is 80 db SPL. This would simply be what you get
when you hook up the noise to a meter of some sort. Now, the next
step is not that easy in practice, but easy in principle. You've got
to get the "spectrum level" of the noise at the frequency where your
noise is at its peak (or in the flat region, if you've got something
like a butterworth filtered noise. To get the spectrum level you must
pass the noise (at the output of your filter) through some kind of
filter whose properties you know exactly. Some spectrum analyzers
have 10 Hz "square filters" for example. If the noise reads 30 dB SPL
at the output of, say, a 10 Hz square filter, then the spectrum level
is 70 - 10 log 10 or 60 dB SPL. So, you've got a noise with a total
power of 80 and a spectrum level of 60. Since the total power is
equal to the spectrum level times the equivalent square bandwidth
(that's how I got 70 - 10 log 10 = 60 above), then you now know your
equivalent square bandwidth is 80-60 = 20 in dB terms, or, taking the
antilog, 100Hz.

Israel Nelken wrote :

       The equivalent rectangular bandwidth (I assume this is what you mean)
is equal to the sum over all frequencies of the energy of your noise band,
divided by the spectrum level at the peak of your noise band.
Re critical bands: the basic papers were written by Pickles (1975) and
Costalupes (1983). I believe Eric Young has copies, at least of the Costalupes

Here's what I got concerning critical bandwidth in cats :

Donald Greenwood wrote :

The first two papers review quite a bit of data on frequency-position
functions and human critical bandwidth estimates and what function
fits them quite well.  Then Part II of 1991 paper reviews some CB
data on other species.

The discussion in the second part of the1991 paper republishes the
cat data of the Pickles, Nienhuys and Clark, and Watson papers and
will assist in understanding those data.  Pickles' reinterpretation
of Watson's data (which I repeat in the 1991 paper) is probably right.

See also Schreiner's estimates (from inferior colliculus neural data)
of what critical bands may be in the cat.  He forgot to compare my
function to the data, but I have a modified figure (somewhere)
showing my cat function goes right through the center of gravity of
their data with nearly the same slope and magnitude.  You will be
able to "see" that without the figure since (1) Schreiner compares
Pickles and Nienhuys-Clark data to the neural data and (2) the 1991
paper above compares the function to the Pickles and Nienhuys-Clark

In comparing across species bear in mind the 1996 paper in Hearing Research.

Greenwood, D.D. (1990)  A cochlear frequency-position function for
several species - 29 years later. J. Acoust. Soc. Am. 87, 2592-2605.
Greenwood, D.D. (1991)  Critical bandwidth and consonance in relation
to cochlear frequency-position coordinates, Hear. Res. 54, 164-208.
Greenwood, D.D. (1996) "Comparing octaves, frequency ranges, and
cochlear-map curvature across species, Hearing Reseach, 94, 157-162.
Greenwood, D.D. and Maruyama, N. (1965)  Excitatory and inhibitory
response areas of auditory neurons in the cochlear nucleus.  J.
Neurophysiol. 28, 863-892.  [This paper plots tuning curves and rate
contours on cat frequency-position function of that time.  That
earlier function has same normalized slope constant as current cat
f-p function.]
Nienhuys, T.G.W. and Clark, G.M. (1979)   Critical bands following
the selective destruction of cochlear inner and outer hair cells.
Acta Otolaryngol. 88, 350-358.
Pickles, J.O. (1975)  Normal critical bands in the cat.  Acta
Otolaryngol. 80, 245-254.
Pickles, J.O. (1976)  Role of centrifugal pathways to cochlear
nucleus in determination of critical bandwidth.  J. Neurophysiol. 39,
Pickles, J.O. (1979)  Psychophysical frequency resolution in the cat
as determined by simultaneous masking and its relation to
auditory-nerve resolution.  J.Acoust. Soc. Am. 66, 1725-1732.
Pickles, J.O. and Comis, S.D. (1973)  Role of centrifugal pathways to
cochlear nucleus in detection of signals in noise.  J. Neurophysiol.
36, 1131-1137.
I am not sure that the last Pickles, et al paper is relevant but its
inclusion won't hurt and any relevance will be discussed in 1991
paper above.

Schreiner, Christoph -  Can't recall reference.  About five years
ago.  Suggest you ask him for it.  Christoph Schreiner
Watson, C. S. (1963)  Masking of tones by noise for the cat.  J.
Acoust. Soc. Am. 35, 167-172.

Jont Allen wrote :

This was done at Johns Hopkins by John Costalupes in 1983.
He did it both neurally and psychophysically, on the cat.

      AUTHOR = "John A. Costalupes",
      TITLE = "Broadband Masking Noise and Behavioral Pure Tone
                        Threshold in
      YEAR = "1983",
      VOLUME = 74,
      NUMBER = 3,
      PAGES = "758--764",
      MONTH = "September"}

Ask Eric Young about this, or Murray Sachs. You can
read my summary in JASA, Vol. 99, #4, April 1996, Figure 5.
It seems to me there was a paper with Eric as well.

In humans, the critical ratio is independent of level
over a 60 dB dynamic range. This was shown first by (you
guest it folks) Harvey Fletcher in 1938, Proc.. Nat. Acad.
Sci.  vol. 24 pp 265-274. The experiment was repeated by
Hawkins and Stevens (1950) with the same result JASA v22
pp 6-13.

Pickles also did the experiment, but he told me there were
some problems with the result. I dont remember what exactly.

        AUTHOR = "J. O. Pickles",
        TITLE = "Normal Critical Bands in the Cat",
        JOURNAL = "Acta Otolaryngol",
        YEAR = "1975",
        VOLUME = 80,
        PAGES = "245-254"}

This is a really important problem, with a lot of controversy.
Ask 5 people and you will get 5 different answer.

Erv Hafter wrote :

Check out Miller and Watson (or Watson and Miller), circa
1962.  Hi to Brad.

Matt wrote :

You should look at some papers by D.D. Greenwood in both the JASA and
Hearing research. If you can't find the references then I could rustle
them up.

Gilad Jacobson wrote :

You should take a look at
Pickles, 1979     (JASA 66(6))
Costalupes, 1983  (JASA 74)
Good luck!

William Yost wrote :

The best book covering psychophysical measures on all animals is the
Handbook of Animal Psychophysics. It has tables and graphs of every
type of pyschophysical measure on all animals. contact Dick Fay at


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Barbara S. Muller, PhD.                         Email : bmuller@bme.jhu.edu
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