Abstract
In this paper, we propose a method to estimate a correlation coefficient of two correlated complex signals on the condition that only the amplitudes are observed and the phases are missing. Our proposed method is based on a maximum likelihood estimation. We assume that the original complex random variables are generated from a zero-mean bivariate complex normal distribution. The likelihood of the correlation coefficient is formulated as a bivariate Rayleigh distribution by marginalization over the phases. Although the maximum likelihood estimator has no analytical form, an expectation-maximization (EM) algorithm can be formulated by treating the phases as hidden variables. We evaluate the accuracy of the estimation using artificial signal, and demonstrate the estimation of narrow-band correlation of a two-channel audio signal.
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Acknowledgment
This work was supported by JSPS KAKENHI Grant Number 23240023.
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© 2015 Springer International Publishing Switzerland
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Miyabe, S., Ono, N., Makino, S. (2015). Estimating Correlation Coefficient Between Two Complex Signals Without Phase Observation. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_49
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DOI: https://doi.org/10.1007/978-3-319-22482-4_49
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