Coarticuration is important in speech recognition or synthesis of connected speech. Therefore, in the study of connected speech, speech unit should be considered from the viewpoint of the coarticuration. In this paper, combination of two phonemes are considered as the unit mentioned above and called a phoneme dyad. The reversibility of phoneme dyad is noticed in this paper to study its nature. Reversible dyad means that we can listen to /sa/ when /as/ is reproduced reversely. Identification experiments have been done for 120 subjects. In these experiments, we analyzed the nature of reversibility of phoneme dyad by taking the following points into consideration: (1) The question is whether the reversibility of phoneme composed of the same consonant can be influenced by the vowel. (2) In case of occurring a confusion, is there any rule? What is the cause for the rule? (3) How does the reversibility of consonant change as to words or meaningless spellings? As a result, the facts mentioned below were found out. Phoneme dyads composed of vowels or /s/ are reversible. Phoneme dyads composed of voiceless stops like /k/ are not reversible. Nevertheless, voiceless stops in a word sometimes can be heard when a word that has been recorded reversely is reproduced reversely. This shows that the information proper to human is important in case of understanding the word. There was a tendency that confusion happens among the phonemes which have the same place of articuration. This tendency is noticeable especially as to stops, and shows that an information at the place of articuration is reversible.
In many fields of research, there naturally arise many problems such as whether echoes exist or not in time series and how is their timing, and there exist many problems easily convertible to the form mentioned above. The use of correlation technique or Cepstrum analysis has proved powerful to solve these problems. However, it is difficult to detect an echo by those techniques under such conditions as the band width of the time series is not wide enough and the delay time of the echo is small. This paper presents a new method which is useful even under these conditions. The new method is based on the principle that an echo shows up as s delta function in the impulse response function of the optimum predictor for the signal containing the echo. In the simplest echo, values of a time series y(t) are multiplied by a constant a(|a|<1), delayed by a time difference σ, and added to the original series to give a new series as given by Eq. (1). The transfer function of the optimum predictor H(jω) for the signal is given by Eq. (11), where α is the prediction time. Its inverse Fourier transform or the impulse response function h(τ) is given by Eq. (14) and also shown schematically in Fig. 1(b). A train of delta functions is contained in h(τ) and the biggest delta function gives us the information about the echo. Namely, its position and height correspond to the timing (σ-α) seconds and the intensity a respectively. Then this prediction method converts the detection problem of the echo into that of the delta function in the impulse responce function of the predictor. This transformation brings forth an enormous advantage that the delta function showing the existence of the echo is too sharp to be covered up by other noisy terms in the impulse response function and then can be scarcely overlooked even if the signal band width is narrow and/or if the time delay of the echo is small. Simulation results (Fig. 2), experiments of sound propagation in an anechoic room (Fig. 4) and those of flexural wave propagation in a steel strip (Fig. 6) show the effectiveness of this prediction method.