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Re: envelope extraction

Ben, if what you're looking for is envelope extraction, then there's no reason to prefer half-wave to full-wave rectification; use a time constant consistent with the needs of your application; in speech recognition, 50 Hz is consistent with smoothing away pitch effects, pretty much.

The half-wave rectifier makes sense if you wan to model and use the sort of fine temporal structure that the cochlea sends up the auditory nerve to the brain. It's capable of representing details up to a couple of kHz at least, and half-wave is needed to keep a consistent represenation of different types of pitch, and to agree with known physiology. A filter corner around 1.5 kHz is typical, I think. I haven't looked at refs on this for a long time, but I always had the impression that the psychophysics implied a wider band than the physiologists were able to observe. I don't know if it's settled.