We use a mixture of circular-symmetric complex-Gaussian distributions projected on the unit hy-persphere for modeling the complex discrete Fourier transform coefficients of noisy speech signals in the frequency domain. According to the derived mixture model, clustering of the noise and the target ...
SNR was estimated fitting a Gaussian profile to the CPL peaks associated with a given transition. For the 5D0→7F1 transition (595.2 nm) SNR recovered by the SM-CPL was 18, whereas SNR recovered by the SS-CPL spectrometer was 148. For the SM-CPL spectrometer to yield a similar SNR...
Negation of a circular value is the symmetric value relative to z (the zero-value). Opposite operator (~c) is defined for any circular value. The result is a circular value.Opposite of a circular value is the circular value pointing to the opposite direction. Addition and subtraction ...
A circularly polarized Gaussian pulse traversing a time interface is also studied. If the wave-vector spectrum of a pulse mainly concentrates in the non-traveling-wave band, the pulse will be trapped with nearly fixed center while its intensity will grow rapidly. In addition, we propose an ...
where theN×Nmatrixcmis the elevation-dependent MCM. Due to the circular symmetry, a model for the MCM of UCAs [5,7,20] can be a complex symmetric circulant matrix. In this article, we only considerN= 2K+1. Therefore,Cmcan be expressed as ...
because of the fact that the circular nano-aperture is mirror-symmetric and the incidence is normal, the CD is very close to zero when the incident beam is Gaussian (q=0). The residual CD can be attributed to small asymmetries on the sample or the incoming beam. When vortex beams withq...
∠z denotes the phase of a complex number z, CN(μ,σ2) represents a complex Gaussian distribution with mean μ and variance σ2 while a Gaussian distribution with mean μ and variance σ2 denotes as N(μ,σ2); the expectation of a random variable is denoted as E⋅ while the matrix...
6 Finally, a CD spectrum is obtained by centering a band function, such as a Gaussian or a Lorentzian curve, around the rotational strengths calculated for the specific transition energies. An Example Matrix Method Computation As an example of a matrix method computation, consider the nπ∗ ...
Eq. 16.20 is the Hagen-Poiseuille flow profile for the rotationally symmetric tube or pipe. It is a parabolic profile with the maximum velocity at the center of the tube. In order to visualize this equation, we define a helper function v2 in line 10. This new function will take the r ...
We note that for real τ this is precisely the normalization constant CN,β(τ), from (9), for the Hua–Pickrell β-ensemble, but for complex τ these constants differ. In a similar spirit, for ℜ(τ)>−12, we define the linear operator EN,β(τ), acting on symmetric functions...