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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Complex normal distribution ： ウィキペディア英語版 Complex normal distribution In probability theory, the family of complex normal distributions characterizes complex random variables whose real and imaginary parts are jointly normal. The complex normal family has three parameters: ''location'' parameter ''μ'', ''covariance'' matrix Γ, and the ''relation'' matrix ''C''. The standard complex normal is the univariate distribution with ''μ'' = 0, Γ = 1, and ''C'' = 0. An important subclass of complex normal family is called the circularly-symmetric complex normal and corresponds to the case of zero relation matrix and zero mean: $\backslash mu\; =\; 0\; \backslash \; \backslash text\; \backslash \; C=0$.〔( ''bookchapter, Gallager.R'' ), pg9.〕 Circular symmetric complex normal random variables are used extensively in signal processing, and are sometimes referred to as just complex normal in signal processing literature. ==Definition== Suppose ''X'' and ''Y'' are random vectors in R''k'' such that vec(Y'' ) is a 2''k''-dimensional normal random vector. Then we say that the complex random vector : $$ Z = X + iY \, has the complex normal distribution. This distribution can be described with 3 parameters: : $$ \mu = \operatorname(), \quad \Gamma = \operatorname(), \quad C = \operatorname(), where ''Z'' ′ denotes matrix transpose, and Z denotes complex conjugate. Here the ''location'' parameter ''μ'' can be an arbitrary k-dimensional complex vector; the ''covariance'' matrix Γ must be Hermitian and non-negative definite; the ''relation'' matrix ''C'' should be symmetric. Moreover, matrices Γ and ''C'' are such that the matrix : $$ P = \overline\Gamma - \overline'\Gamma^C is also non-negative definite.〔 Matrices Γ and ''C'' can be related to the covariance matrices of ''X'' and ''Y'' via expressions : $\backslash begin$ & V_ \equiv \operatorname() = \tfrac\operatorname(+ C ), \quad V_ \equiv \operatorname() = \tfrac\operatorname(+ C ), \\ & V_ \equiv \operatorname() = \tfrac\operatorname(+ C ), \quad\, V_ \equiv \operatorname() = \tfrac\operatorname(- C ), \end and conversely : $\backslash begin$ & \Gamma = V_ + V_ + i(V_ - V_), \\ & C = V_ - V_ + i(V_ + V_). \end 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Complex normal distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.