Subject: Re: Gaussian vs uniform noise audibility From: Israel Nelken <israel(at)MD.HUJI.AC.IL> Date: Fri, 23 Jan 2004 07:21:48 +0200I think that one has to distinguish between the spectral representation as a tool for describing signals on the one hand, and the question of whether the ear is a fourier analyser. For the second question, I think everyone's answer (certainly mine) is strictly speaking no - although spectrograms are reasonable 0th order approximations to what we hear... For the first question, spectral representation is mathematically 'true' (within the obvious limits of the application of a mathematical theory to real life). Furthermore, for real-life signals the inverse fourier transform is equal to the original function almost everywhere, so that any operation on the signal that is formulated in terms of its temporal waveform can be also formulated in terms of the fourier spectrum (amplitdue AND phase). Some of these operations may be vastly more complicated when described in the spectral domain, but this does not invalidate the above statement. In these terms, there's a full equivalence between time and spectral processing. Finally, there's the question of the usefullness of the spectral description of random processes, which is yet a somewhat different question. The independence of the spectral components of a gaussian process is a mathematical result, independent of the physiology of hearing, but it has consequences for hearing. Since we are sensitive to spectral correlations, non-gaussianity can be detectable by such sensitivity. This doesn't assume anything about the use of Fourier transforms in the ear! Eli -- ================================================================== Israel Nelken Dept. of Neurobiology The Alexander Silberman Institute of Life Sciences Edmond Safra Campus, Givat Ram | Tel: Int-972-2-6584229 Hebrew University | Fax: Int-972-2-6586077 Jerusalem 91904, ISRAEL | Email: israel(at)md.huji.ac.il ==================================================================