Data Handling Methodology for Discrete Wavelets and Its Applications to the Dynamic Vector Fields

Abstract

A discrete wavelet transform is one of the effective methodologies for compressing the image data and extracting the major characteristics from various data, but it always requires a number of target data composed of a power of 2. To overcome this difficulty without losing any original data information, we propose here a novel approach based on the Fourier transform. The key idea is simple but effective because it keeps all of the frequency components comprising the target data exactly. The raw data is firstly transformed to the Fourier coefficients by Fourier transform. Then, the inverse Fourier transform makes it possible to the number of data comprising a power of 2. We have applied this interpolation for the wind vector image data, and we have tried to compress the data by the multiresolution analysis by using the three-dimensional discrete wavelet transform. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.

A Proposal of Flat Transformers

“…The magnetic field vector distributions are generally three dimensional vectors. Therefore, when we apply the wavelets multi-resolution analysis to the three dimensional vectors, it leads to the three-dimensional vector wavelets transform [2,3].…”

“…Apply the discrete wavelets transform to the magnetic field vector distributions around the transformer having open magnetic flux paths clarifies that the dish like ferrite cores embedding spirally wound coils gives a far excellent magnetic field vector distribution compared with those with conventional U shape cores [2,3]. An extension of conventional inner core type trans-former employing U shape cores spreads the magnetic fields around the transformer centred at the air gaps.…”