接下来我们将注意力放在这样的信道上:在离散时间连续无记忆信道 (定义 9.4) 的基础上,我们进一步要求信道的噪声是可加 (additive) 的 Gaussian 白噪声 (white noise),且采用平均功率约束。具体而言:对于时刻 i=1,2,\ldots, ,信道输入为 X_i ,那么信道输出就是 Y_i=X_i+Z_i\\其中\{Z_i\}_{i=1
x1 =gnoise(sqrt(sig1sq))// Gaussian random generatorx2 =gnoise(sqrt(sig2sq))Y1 =(x1 + x2)/sqrt(2)// joint (CORRELATED) dataY2 =(x1 - x2)/sqrt(2)// obeying given pdfBiHistSetBins(Y1, Y2,201, -5,0.05,201, -5,0.05,"BivariateHistWave")BivariateHistWave =log(BivariateHist...
where zt and zt+1 are the states at time instant t and t+1, respectively, yt and ut are process outputs and inputs, respectively and εt and et are the additive noise in zt+1 and yt. The model parameters are given by Ω1, Ω2, Ω3 and Ω4. The BN representation of the SSM...
A Gaussian process (GP) is a continuous collection of random variables, any finite number of which have a joint Gaussian distribution. More formally, a GP, which we will denote by Y, is a distribution over functions whose values on X≡x1,…,xn have a multivariate normal probability density...
Gaussian blurringis a non-uniform noise reductionlow-pass filter(LP filter). The visual effect of this operator is asmooth blurry image. This filter performs better than other uniform low pass filters such asAverage filter (Box blur).
Gaussian random fields have a long history in science that dates back to the research of Andrey Kolmogorov and his group. Their investigation remains an active field of research with many applications in physics and engineering. The widespread appeal of
b Comparison of the integrated absolute error when the next measurement point is selected using the maximal uncertainty in GP reconstruction versus when the next measurement point is selected randomly (for three different pseudo-random seeds). c Exploration path in xy coordinates for the first 60 ...
Brownian motion is also a Gaussian process. It follows a Gaussian random walk, with diffusion occuring at each time point driven by a Gaussian input. This implies it is both Markov and Gaussian. The covariance function for Brownian motion has the form ...
For each time point of interest, we add a random variable to the Gaussian process. With n time points, there are therefore n corresponding random variables in the Gaussian process. The latent function is given by the values taken by these random variables (Fig. 1a). Without losing any ...
For example, yC denotes that the response vector y is random with respect to case C, and yc denotes the observed response vector from a fixed case c. In addition, we will use some common vectors and matrices: I represents an identity matrix, O a matrix of zeroes, and 0 a vector of ...