complex Gaussian random variable60B1562E10We prove the following theorem. Let α = a + i ? b {\\alpha=a+ib} be a nonzero complex number. Then the following statements hold: (i) Let either b ≠ 0 {beq 0} or b = 0
The normal or Gaussian distribution is often denoted byN(μ,σ2)N(μ,σ2). When a random variableXXis distributed normally with meanμμand varianceσ2σ2, we writeX∼N(μ,σ2)X∼N(μ,σ2). The formula for the distribution is ...
From this theorem, we can derive an equation for the characteristics of the jump process as follows: Using the relation for the Gaussian random variable ξ and the last relation in Eq. (5), with j = 4 and j = 6, we first estimate the jump amplitude and then the jump rate ...
the hidden vector in the model graph is a Gaussian distributed random variable \({Z}_{k}\), the fusion coding \({\varepsilon }_{tar}\) is connected with the context vector \({V}_{C}\), so that the decoder can generate different motion contours. so that the decoder can generate ...
To simulate the various SNR conditions, an “analysis signal” is generated by adding a random complex additive white Gaussian Noise (AWGN) signal to the collected complex signal. Before adding, the noise signal is filtered and power-scaled to achieve desired SNR for the analysis signal. Next,...
For the complex networks under consideration, the random occurrences of the faults, the missing measurements and the switching outer-coupling configuration matrices are governed by mutually independent Bernoulli distributed white sequences. Moreover, the Gaussian white noise sequences are utilized to ...
1 The number a + bi is said to be a standard complex Gaussian if a and b are independent, normally distributed random variables with mean 0 and variance 1/2 [24, Definition 24.2.1]. 123 Cuts and semidefinite liftings for the complex cut polytope Table 4 Average rate and computation ...
/2nn! ξ2 n for the Gaussian random variable ξ and the last relation in Eq. (5), with j = 4 and j = 6, we first estimate the jump amplitude σξ2 (x, t) and then the jump rate λ(x, t) as: σξ2 (x, t) = M (6)(x, 5M (4)(x, t) t) ...
Since the artificial neural network does not pro- vide an estimated prediction variance, as Gaussian processes do, it has been computed using jackknife resampling technique, which consists in training repeatedly the model by resampling one observation each time. In [9] a random forest has been ...
The hydrodynamic equations, averaged for the Gaussian variables, for the non-reciprocal TSAIM read: $${\partial }_{t}{\rho }_{s}={D}_{xx}{\partial }_{x}^{2}{\rho }_{s}+{D}_{yy}{\partial }_{y}^{2}{\rho }_{s}-v{\partial }_{x}{m}_{s},$$ (12) ...