Abstract
This chapter describes spectral peak selection used in estimating the true spectrum of the target sequence, which is assumed to be composed of sinusoidal sequences. A compound sinusoidal sequence can be identified by repeating spectral peak selection from the interpolated spectral sequence iteratively independent of the observation length, provided the sinusoidal components are time independent. The frame-wise approach of spectral peak selection can also be applied to the estimation of fundamental frequencies of music tones. This chapter also describes clustered line-spectral modeling (CLSM) formulated to estimate the frequency components of a sequence composed of densely clustered sinusoidal components. CLSM is one approach to represent a sequence the envelope of which carries the signal signature. A finite-approximation to the Weierstrass function, which is an example of a harmonic sinusoidal sequence on the logarithmic frequency scale, is an interesting example to apply spectral peak selection. Spectral peak selection is also one approach to perform extrapolation (or prediction) of the target sequence outside its observation range.
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Tohyama, M. (2015). Sinusoidal Representation of Sequence. In: Waveform Analysis of Sound. Mathematics for Industry, vol 3. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54424-1_8
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DOI: https://doi.org/10.1007/978-4-431-54424-1_8
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