A Sparse Decomposition Method for Periodic Signal Mixtures

Nakashizuka, Makoto

doi:10.1093/ietfec/e91-a.3.791

Cited by 8 publications

(9 citation statements)

References 11 publications

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“…First, an initial estimate of the -th period correspondence is obtained from the estimated instantaneous period in a recursive manner as (23) Next, lower and upper bounds of the -th period correspondence, namely, the boundaries of the so-called corridor of a DTW path search region, are set to (24) …”

Section: Self Dtwmentioning

confidence: 99%

Phase Estimation of a Single Quasi-Periodic Signal

Makihara

Aqmar

Trung

et al. 2014

IEEE Trans. Signal Process.

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We propose a method for phase estimation of a single non-parametric quasi-periodic signal. Assuming signal intensities should be equal among samples of the same phase, such corresponding samples are obtained by self-dynamic time warping between a quasi-periodic signal and a signal with multiple-period shifts applied. A phase sequence is then estimated in a sub-sampling order using an optimization framework incorporating 1) a data term derived from the correspondences and 2) a smoothness term of the local phase evolution under 3) a monotonic-increasing constraint on the phase. Such a phase estimation is, however, illposed because of combination ambiguity between the phase evolution and the normalized periodic signal, and hence can result in a biased solution. Therefore, we introduce into the optimization framework 4) a bias correction term, which imposes zero-bias from the linear phase evolution. Analysis of the quasi-periodic signals from both simulated and real data indicate the effectiveness and also potential applications of the proposed method.

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Section: Self Dtwmentioning

confidence: 99%

Phase Estimation of a Single Quasi-Periodic Signal

Makihara

Aqmar

Trung

et al. 2014

IEEE Trans. Signal Process.

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“…This term originates in previous work on sparse decompositions of mixtures of periodic sources [6]. It favors sparse solutions in which many sources have zero excitation (i.e., all zero initial conditions, with uiτ = 0 for all τ ); we interpret such sources as inactive.…”

Section: Extension To Autoregressive Modelsmentioning

confidence: 99%

“…Our approach builds on previous work for computing sparse decompositions of mixtures of periodic sources [6]. Specifically, this earlier work considered periodic sources whose periods were integer multiples of the sampling resolution.…”

Section: Special Case: Periodic Signalsmentioning

confidence: 99%

“…Second, we cannot model individual sources by simple static templates because they themselves exhibit many degrees of variability besides amplitude (e.g., duration, phase, timbre). To handle these differences, we have adapted the basic ideas behind basis pursuit to our setting, building also on recent work for mixtures of periodic sources [6]. Like basis pursuit, our approach computes a sparse decomposition of mixed signals in terms of their constituent sources, the possibilities of which are catalogued by a large dictionary.…”

Section: Introductionmentioning

confidence: 99%

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Sparse decomposition of mixed audio signals by basis pursuit with autoregressive models

Cho

Saul

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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We develop a framework to detect when certain sounds are present in a mixed audio signal. We focus on the regime where out of a large number of possible sounds, a small but unknown number are combined and overlapped to yield the observed signal. To infer which sounds are present, we attempt to decompose the observed signal as a linear combination of a small number of sources. To encourage sparse solutions with this property, we balance the modeling errors from individual sources against an 1-norm penalty of the type used in basis pursuit and regularized linear regression with grouped variables. Our approach can be viewed as a novel generalization of basis pursuit in two ways: first, with a dictionary of fixed size, we attempt to model acoustic waveforms of potentially variable duration; second, for dictionary entries, we do not store basis vectors representing static templates, but the coefficients of autoregressive models that characterize the acoustic variability of individual sources. We derive the required optimizations in this framework and present experimental results on combinations of periodic and aperiodic sources.

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“…Our paper builds on recently proposed frameworks for sparse decomposition of mixed audio signals (Nakashizuka, 2008;Cho & Saul, 2009). Previous studies addressed the problem of inference in this framework: given autoregressive models of time domain waveforms for a large number K of possible sources, how to identify which k K of these sources occur in single microphone recordings?…”

Section: Introductionmentioning

confidence: 99%

Learning dictionaries of stable autoregressive models for audio scene analysis

Cho

Saul

2009

Proceedings of the 26th Annual International Conference on Machine Learning

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In this paper, we explore an application of basis pursuit to audio scene analysis. The goal of our work is to detect when certain sounds are present in a mixed audio signal. We focus on the regime where out of a large number of possible sources, a small but unknown number combine and overlap to yield the observed signal. To infer which sounds are present, we decompose the observed signal as a linear combination of a small number of active sources. We cast the inference as a regularized form of linear regression whose sparse solutions yield decompositions with few active sources. We characterize the acoustic variability of individual sources by autoregressive models of their time domain waveforms. When we do not have prior knowledge of the individual sources, the coefficients of these autoregressive models must be learned from audio examples. We analyze the dynamical stability of these models and show how to estimate stable models by substituting a simple convex optimization for a difficult eigenvalue problem. We demonstrate our approach by learning dictionaries of musical notes and using these dictionaries to analyze polyphonic recordings of piano, cello, and violin.

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A Sparse Decomposition Method for Periodic Signal Mixtures

Cited by 8 publications

References 11 publications

Phase Estimation of a Single Quasi-Periodic Signal

Phase Estimation of a Single Quasi-Periodic Signal

Sparse decomposition of mixed audio signals by basis pursuit with autoregressive models

Learning dictionaries of stable autoregressive models for audio scene analysis

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