Shifted Independent Component Analysis

Delayed mixing is a problem of theoretical interest and practical importance, e.g., in speech processing, bio-medical signal analysis and nancial 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 in the time domain corresponds to a multiplication of e i! 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 prune to local minima and di culties arise especially in the presence of large delays and high frequency sources. A Matlab implementation can be downloaded from [1].