Abstract
Delayed mixing is a problem of theoretical interest and practical importance, e.g., in speech processing, bio-medical signal analysis and financial data modelling. Most previous analyses have been based on models with integer shifts, i.e., shifts by a number of samples, and have often been carried out using time-domain representation. Here, we explore the fact that a shift τ in the time domain corresponds to a multiplication of e − iωτ in the frequency domain. Using this property an algorithm in the case of sources≤sensors allowing arbitrary mixing and delays is developed. The algorithm is based on the following steps: 1) Find a subspace of shifted sources. 2) Resolve shift and rotation ambiguity by information maximization in the complex domain. The algorithm is proven to correctly identify the components of synthetic data. However, the problem is prone to local minima and difficulties arise especially in the presence of large delays and high frequency sources. A Matlab implementation can be downloaded from [1].
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Keywords
- Independent Component Analysis
- Sparse Code
- Blind Source Separation
- Shift Invariant Subspace
- Convolutive Mixture
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Mørup, M., Madsen, K.H., Hansen, L.K. (2007). Shifted Independent Component Analysis. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_12
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DOI: https://doi.org/10.1007/978-3-540-74494-8_12
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