FourierTransform[expr, t, \[Omega]] 给出 expr 的符号傅里叶变换. FourierTransform[expr, {t1, t2, ...}, {\[Omega]1, \[Omega]2, ...}] 给出 expr 的多维傅里叶变换.
#q-Fourier Transform is not Invertible. Hilhorst's Invariance Principle#Representation Formulas for "The Inverseq-Fourier Transform"#Multidimensionalq-Fourier Transforms#Directq-Fourier Transform of Multivariateq-Gaussian Density Functions#Sequentialq-Fourier Transform of Multivariateq-Gaussian Density Functions#...
Fourier sine transform of the reciprocal of a square root: In[1]:= Out[1]= Compute the Fourier sine transform of a multivariate function: In[1]:= Out[1]= Plot the function and its transform: In[2]:= Out[2]= Compute the transform at a single point: In[1]:= Out[1]= ...
Figs. 2.6C and D show that the transform of the Gaussian function is another Gaussian function, this illustrates linearity (for linear systems it is Gaussian in, Gaussian out which is another version of GIGO). Fig. 2.6E is a single point (the delta function) which has a transform that ...
Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an anal... Xinyue,Du,Daomu,... - 《Applied Optics》 被引量: 43发表: 2006年 Quantization errors in the fast Fourier transform When a fast ...
Despite the fast Fourier techniques itself, there is also the advantage of this transform to be parallelized efficiently, yielding faster versions than the one-dimensional Fourier transform. These properties of the lattice can further be used to perform a fast multivariate wavelet decomposition, where ...
Time Fourier Transform (TFT) is a signal processing tool that focuses on analyzing transient phenomena by dividing signals into small segments assumed to be stationary for analysis, providing spectral contents as a function of time. AI generated definition based on: Sustainable Computing: Informatics ...
Based on the Hermite-Gaussian formulation, it is shown that the complex ABCD optical systems which satisfy a certain condition can be used to realize complex-order Fourier transforms and fractional-order Fourier transforms in real ABCD optical systems are the special case of this framework. Two sim...
We use the usual convention of summation on repeated Latin indices. Domain \(\Omega \) is occupied by a heterogeneous and anisotropic elastic random medium for which the elastic properties are defined by the fourth-order tensor-valued non-Gaussian random field . Let be the \({\mathbb {R}}...
Introducing 2M real and imaginary parts of cak as discrete real-valued input and output, X and Y correspondingly, one gets for the input–output conditional PDF the multivariate Gaussian distribution with the 2M Â 2M quadrature correlation matrix Æ^ whose elements are obtained from the ...