A matrix formulation a the DFT of complex even and complex odd sequences will be presented and, respectively, for each one of the two type of sequences a cosine and a sine based matrix will be used.
Recursive expressions for the two matrices will be obtained and it will be shown that the recursive terms involves only both the same cosine and sine matrices, of halved dimension.
The structure of the algorithm is suitable for parallel hardware implementation.
discrete Fourier transform
FFT even sequences
FFT odd sequences
A quasiharmonic field is a pair $\Cal{F} = [B,E]$ of vector fields verifying $div B=0$, $curl E=0$, and coupled by a distorsion inequality. For a given $\Cal {F}$, we construct a matrix field $\Cal{A}=\Cal{A}[B,E]$ such that $\Cal{A} E=B$. This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator $\Cal {A}[B,E]$ and find applications of them to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
The scope of this work has been to apply multidimensional data visualization techniques to the study of the ancient building decay events. With this aim we have created new visual tools based on the shape variation (glyph), that with more traditional techniques based on the color have been implemented in object-oriented software programs using the innovative and powerful visualization toolkit (VTK), a free C++ class library for visualization and 3D computer graphics. The data used are climatic, chemical and environmental measurements detected on/near the Roman theatre in the city of Aosta, acquired in the ambit of an Italian research project focused on the restoration of ancient monuments
