Abstract
The temporal nature of a sequence is observed in narrow-band envelopes or frame-wise spectra. The envelopes represent the temporal changes in macroscopic structures, whereas the frame-wise spectral properties can be interpreted as related to the time-dependent fine structure of a sequence. The local behavior of phase spectral records or group delay is crucial in the construction of the envelopes. Inspired by the methods used for group delay, triangular window functions are introduced to divide a sequence into short frames. Consequently, the differential (averaging) properties of the spectral functions are formulated in terms of triangular with a positive (negative) slope windowing. Moreover, the short-term auto-correlations are obtained keeping its non-negative Fourier transform. Taking the causal part of the short-term autocorrelation sequence yields the complex power spectral function, the magnitude of which gives the temporal change in the power spectral envelope.
The original version of this chapter was revised.
An erratum to this chapter can be found at DOI 10.1007/978-4-431-54424-1_10
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Tohyama, M. (2015). Temporal and Spectral Characteristics of Discrete Sequence. In: Waveform Analysis of Sound. Mathematics for Industry, vol 3. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54424-1_3
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DOI: https://doi.org/10.1007/978-4-431-54424-1_3
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