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Abstract

A definition of discrete evolutionary spectra is given thatcomplements the notion of evolutionary spectral density given by Dahlhaus(Dahlhaus, R.: Fitting time series models to nonstationary processes. Preprint,Univ. Heidelberg, 1992). For processes that have a discrete evolutionary spectrum,the asymptotic behaviour of linear functionals of the periodogram is investigated.The results are applied in a mathematical analysis of Licklider's theory of pitchperception. A pitch estimator based on this theory is investigated with respect tothe shift of the pitch of the residue described by Schouten et al.(Schouten, J.F.,Ritsma, R.J., Lopes Cardozo: Pitch of the residue, J. Acoust.Soc.Am. Vol.34, No.8,1962, 1418-1424).