Linear Processing for Vector-Valued Signals with Vector-Valued Coefficients

讲座名称：Linear Processing for Vector-Valued Signals with Vector-Valued Coefficients

讲座人：夏香根 教授

讲座时间：6月12日10:00

地点：亚博足彩主楼II区-219

讲座人介绍：

夏香根教授现为美国特拉华大学电气与计算机工程系Charles Black Evans 冠名教授，IEEE Fellow。夏教授1997年获美国国家科学基金会青年教授杰出科研基金奖(CAREER Award)；1998年获美国海军研究总署青年科学家奖 (YIP Award)；2001年获得美国特拉华大学工程院杰出青年教授奖。2009-2012任清华大学电子系无线通信Kumar讲座教授团教授， 2009-2013任韩国World Class University （WCU）讲座教授。担任过多个IEEE会刊及国际期刊的编委会成员，如IEEE Wireless Communications Letters, IEEE Transactions on Signal Processing，IEEE Transactions on Wireless Communications，IEEE Transactions on Mobile Computing, IEEE Transactions on Vehicular Technology，IEEE Signal Processing Letters, Signal Processing (EURASIP)，EURASIP Journal of Applied Signal Processing，Journal of Communications and Networks (JCN), Science China (Information Sciences), Signal Processing (China) 等。

讲座内容：

In this talk, we first introduce arithmetics (+, ―, ×, ÷) for real vectors of any fixed dimension, which are similar to those for real numbers. It can be thought of as a generalization of complex numbers that are just two dimensional real vectors. This is based on rational vector approximations and arithmetics for rational vectors, and can be done via algebraic number fields. Then, we introduce complex conjugate for a real vector and inner product for two real vectors and two real vector-valued signals of finite length. We also define convolution of two real vector-valued signals of finite length. With these concepts, the conventional linear filtering, least squares fitting, and ARMA model for scalar-valued signals can be easily generalized to real vector-valued signals, which broadens the existing linear signal processing methods for scalar-valued signals and might open a door to the future signal processing.

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