Least-Squares Estimation of the Extrema in the Narrow-Band Music Data

The aim of this study is to estimate the maximum and minimum data of the 10-channel music waveforms, each of which contains the spectro-temporal information with a pass-band of one octave at a conventional rate of 44.1 kHz. The least-squares estimation by using a parabola function has approximated the upper or lower half of a period of the filtered waveform, so that 88.1% of the extrema measured in ad- vance has significantly reduced phase error at a bandwidth of channels 3 to 9 (80-10,240 Hz) and also the quantization error for channels 7, 8 and 9 (2,560-10240 Hz). Because the small amplitude for 9.44% of the measured extrema is the primary impediment to the estimation, the neighboring data series around the peaks and/or valleys of the narrow-band waveform is locally regarded as a simple and symmetric structure, which is supported by the auto-regression (AR) process. It is suggested that the appearance of the extrema in the filtered waveform is plausibly predictable in the human auditory system, and the extremal informa- tion plays a key role in encoding the acoustic structure, i.e., the phase-lock discharge in the acoustic nerve.

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