Problems and pitfalls in pitch estimation of infant cries and voice signals

Accurate frequency determination is an usual task in many scientific fields including medical physiological measurements like EEG, ECG and also the determination of the fundamental frequency in acoustical signals. Beyond the pure computational problem the difficulties are connected with ambiguities in the definition of frequency. In the strongest mathematical sense frequency is only defined in exact periodical signals. Unfortunately, most realistic signals are instationary signals which contain no exact periodicities. A certain reasonable degree of idealisation and/or approximation is necessary to reconcile a strong periodicity definition with fast time-varying features of a voice signal. In all these cases the applied frequency determination algorithm defines a special notion of frequency and the resulting frequencies or melodies can be remarkably different. Different signal representations (time-, spectral-, lag-domain, complex demodulation, timefrequency representations) have its characteristic approaches for frequency determination and its specific error sources. Some typical examples are illustrated and discussed. In the time domain there are three main approaches for frequency determination algorithms: The model approach, the correlation approach, and the feature analysis approach. The most common approach is to define a model of one period (with time dependent parameters) and than to fit this model to the data. Examples are the fit of exponentially decreasing or increasing signals. Other well-known approaches contain as models harmonic sets of signals as for example Fourier-analysis etc. A consequent extension of this approach is wavelet-analysis which has simply some more free parameters and uses a band-filtering scheme to generate spectrograms. All these approaches need elementary models/structures ( for example mother wavelets) to be identified in the given signal. The more specific the models the more are the resulting melodies depending from the models. All the well-known problems of parameter identification are also present in frequency determination. The model based approaches are well-suited for longer signals with many repetitions of changing resp. instationary periods. Some typical examples of frequency determination using models and parameter identification are discussed.