Subject: Re: Hilbert envelope bandwidth From: Yadong Wang <ydwang(at)ELE.URI.EDU> Date: Fri, 8 Oct 2004 13:55:06 -0400Dear 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. Regards 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 frequency? Incidentally, misconception concerning band-limitation is widespread in science. It even led to 'measurement' of signals propagating with superluminal speed. Eckard Blumschein