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Re: Gaussian vs uniform noise audibility
Thank you, John Lazzaro, for pointing me to a rather late 'Malcolm Slaney
with Interval' paper. It shows some details more explicitely than 'ON THE
IMPORTANCE OT TIME - A TEMPORAL REPRESENTATION OF SOUND' 1992. It would be
an eye-opener to me too if I was not already aware that he imagines
autocorrelation based on a cochleagram i.e. subsequent to Frequency
analysis, cf. Fig. 1. Perhaps, this was a main reason for lacking success
of his correlogram. Admittedly, invention of the cepstrum and knowledgeable
application of the Wiener-Chintchine theorem were and still are too unusual
as to get easily accepted.
However, the controversy between Peter Cariani and Christian Kaernbach can
be settled if the many indications in favor of autocorrelation are
attributed to a JOINT autocorrelation combining the essential steps of
monaural signal analysis: Frequency analysis and subsequent rectification
within cochlea, then downsampling by means of multipolar chopper cells
within the cochlear nucleus and finally neural analysis of interval width
presumably via coincidence detection.
Such putative mechanism does not require delay lines within the brain.
Peter is correct: Autocorrelation relates to all-order intervals. Christian
is also correct: After he excluded the first step of autocorrelation, he
found compelling evidence for a weaker mechanism that relates on a
remaining purely temporal code and first-order intervals.
What about magnitude, Slaney himself wrote: 'In general the inverse process
is not so straight forward....Not only it is necessary to recover the lost
First step: estimating a consistent set of phases... looking for the best
The algorithm repeats the last two stages as often as needed'.
Let me repeat: Complex-valued representation requires magnitude as well as
phase. While the traditional spectrogram is not a complete representation
because it omits phase, the natural spectrogram is a fully correct and
fully complete time-frequency pattern. Fourier cosine transform does NOT
At 10:51 24.01.2004 -0800, John Lazzaro wrote:
>Eckard Blumschein writes:
>> Of course, complex representation of a signal requires magnitude as
>> as phase. (Magnitude is always positive while there are positive and
>> negative amplitudes.) This should once again persuade anybody that the
>> inner ear does not perform a complex Fourier transform.
>Malcolm Slaney's review of Pattern Playback techniques:
>was an eye-opener for me -- relatively simple techniques let you invert
>magnitude-only, nonlinearly-processed representations back into
>faithful (if not bit-accurate) audio.
>lazzaro [at] cs [dot] berkeley [dot] edu