Statistical theory of peak detection for human hearing

Abstract

Envelope peaks and peak factors of narrow-band sounds have been found in simulation studies to explain a wide range of experiments on sound discrimination [e.g., J. L. Goldstein, J. Acoust. Soc. Am. 99, 2541(A) (1996)]. To extend understanding of peak detection, mathematical approximations were developed for the first and second moments of log (dB) envelope statistics of a tone centered in noise with duration T and bandwidth W. Noises considered are: uniform periodic noise (UPN) having uniform amplitudes and random phases, Gaussian periodic noise (GPN) having random amplitudes and phases, and true Gaussian noise (TGN). Key properties quantified include: (1) Three nearly independent causes of waveform fluctuation underlie peak variance, viz., phase noise, energy noise, and interaction of tone with common frequency noise (energy cross term). (2) The energy variances in peak detection are similar as for energy detection. (3) Peak factor variance is primarily phase noise, which, for noise alone, is ∼1 dB for T×W>2. (4) Peak and peak factor means differ by mean energy. (5) Mean peak growth for a small tone added to noise follows energy summation, while for a small noise added to a tone, the growth follows rms amplitude summation. [Work supported by NSF Grant IBN-9728383.]