

Re: Hilbert envelope bandwidth

Dear Eckard Blumschein:

Here are my answers to some of your questions.

'Who introduced the term Hilbert envelope?'

The name Hilbert envelope was given by Dennis Gabor. The Hilbert
transform was introduced into electrical
 engineering literatures by Yuk Wing Lee around 1930. Actually 'Lee had
a difficult time convincing the
senior MIT faculty at his doctoral defense of the validity of the
relation. Ultimately it was Wiener's
endorsement of the concept that allowed the work to pass and Lee to
receive his degree. (See Therrien's 2002
article in IEEE Signal Processing Magazine.)

'How to get it? Will it work in ASR?'

To get the Hilbert envelope, the Hilbert operator in the time domain or
halfway rectifier followed by low pass
filtering would normally be used.  A more interesting and practical way
is to model the envelope by an
all-pole model.

Linear prediction in spectral domain (LPSD), a duality of linear
prediction, was developed by Kumaresan
and Rao (JASA 1999). In the mean time, Athineos and Ellis (ASRU 2003),
following the idea of temporal
noise shaping, proposed frequency-domain linear prediction (FDLP) and
applied it successfully to ASR first.

Even more improvement of recognition accuracy was demonstrated in their
most recent paper (Athineos,
Hermansky and Ellis in ICSLP-04), where linear predictive temporal
patterns (LP-TRAP) were introduced.

'Is it important for speech perception?'

In order to understand the relative importance of temporal Hilbert
envelope and fine structure, Smith,
Delgutte, and Oxenham (letter to nature, 2002) performed the famous
chimaeric sounds experiments
and concluded that the envelope is most important for speech perception
with increasing number of filters.
However, some of the technical issues in the design of the experiments
make their conclusion quite dubious.

Any comments are welcome.


Yadong Wang

Yadong Wang,  Postdoctoral Fellow
Cognitive Neuroscience of Language Lab
Dept. of Linguistics
1401 Marie Mount Hall
University of Maryland
College Park MD 20742

-----Original Message-----

Dear Yadong Wang,

Perhaps, I am not the only one here who would like to understand how
Hilbert envelope differs from temporal envelope and what "temporally
flattened" does mean. I am aware of Dan Ellis and others who calculate
squared Hilbert envelope as squared magnitude of the analytic signal in
order to depict hearing as determined by envelope and fine structure
within a number of frequency bands. Smith, Delgutte, and Oxenham (letter
to nature 2002) even spoke of an 'alternative signal decomposition by
Hilbert slowly varying envelope and rapidly varying fine time
structure'. Who introduced the term Hilbert envelope?

I respect those who create new tools. However, I cannot confirm that so
many confusing redundancy in theory is really justified. Let's tear down
a lot of unnecessary sophistication after restricting to either really
elapsed time or time to come after a given point. In other words, let's
abandon the wrong belief that complex calculus must be immediately
merged with frequency analysis. Complex modulator envelopes, as demanded
by Atlas, Li, and Thompson at ICASSP 2004, are only then necessary
prerequisites of unambiguous demultiplication if Fourier transform is
used instead of cosine transform. Isn't it absurd to declare the
modulating signal non-negative but operate with unreal negative

Incidentally, misconception concerning band-limitation is widespread in
science. It even led to 'measurement' of signals propagating with
superluminal speed.

Eckard Blumschein