Application of loudness/pitch/timbre decomposition operators to auditory scene analysis

Abstract

We proposed[1] nonlinear operators which decompose a changing energy of sound in wavelet domain into three orthogonal components: i.e., loudness and pitch as coherent changes, and timbre as incoherent change. We showed that they could detect the discontinuity of a single sound stream with excellent temporal resolution and sensitivity. In this paper, we extend the coherency principle so that it can describe and pursue the individual coherency of non-overlapping sound streams in wavelet domain. It is realized by Parzen's non-parametric estimates and Kalman filtering of loudness change rate and pitch shift rate. Using this method, we show some experiments for extraction of the most salient stream from multiple sound streams.

Auditory scene analysis based on time‐frequency integration of shared FM and AM (I): Lagrange differential features and frequency‐axis integration

“…Figure 9 shows the continuous traces of the stream parameters based on Eq. (26). The initial value is the maximum point which occurred first significantly.…”

Signal Processing Methods for Music Transcription

“…6. Graphical representation of the Gaussian pdf of a scalar (continuous) random variable (left) and a two-dimensional Gaussian random variable (right).…”

“…The mathematical object p(x|^) admits two interpretations: First, when read as a pdf of x for a given 6, p(x|0) is called the conditional pdf of x^ conditioned on 6. Second, when seen as a function of 6 for given x, p(x|0) is called the parameter likelihood function and it is defined over the space of all possible values of 9 denoted O.…”

“…This can however be avoided by modifying the likelihood into a penalized likelihood^ defined as L^W = Lx(0) + Ar? (0), (2.47) where Lx(^) is defined in (2.34) and f2 [6) is aimed at lowering the likelihood in parts of the space © which are to be avoided. ^^ In the Gaussian mixture example where J > m^ the penalty term can be set so as to disable variance parameters that are too small; see [91].…”

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