講座名稱：Linear Processing for Vector-Valued Signals with Vector-Valued Coefficients

講座人：夏香根 教授

講座時(shí)間：6月12日10:00

地點(diǎn)：北校區(qū)主樓II區(qū)-219

講座人介紹：

夏香根教授現(xiàn)為美國(guó)特拉華大學(xué)電氣與計(jì)算機(jī)工程系Charles Black Evans 冠名教授，IEEE Fellow。夏教授1997年獲美國(guó)國(guó)家科學(xué)基金會(huì)青年教授杰出科研基金獎(jiǎng)(CAREER Award)；1998年獲美國(guó)海軍研究總署青年科學(xué)家獎(jiǎng) (YIP Award)；2001年獲得美國(guó)特拉華大學(xué)工程院杰出青年教授獎(jiǎng)。2009-2012任清華大學(xué)電子系無(wú)線通信Kumar講座教授團(tuán)教授， 2009-2013任韓國(guó)World Class University （WCU）講座教授。擔(dān)任過多個(gè)IEEE會(huì)刊及國(guó)際期刊的編委會(huì)成員，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。

講座內(nèi)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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