Tools from Harmonic Analysis
نویسنده
چکیده
The Fourier transform can be thought of as a map that decomposes a function into oscillatory functions. In this paper, we will apply this decomposition to help us gain valuable insights into the behavior of our original function. Some particular properties of a function that the Fourier transform will help us examine include smoothness, localization, and its L2 norm. We will conclude with a section on the uncertainty principle, which says though these transformations are useful there is a limit to the amount of information they can convey.
منابع مشابه
Classical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
متن کاملClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
متن کاملHarmonic Response of Pile Groups to Dynamic Loading
A completely general method of analysis for three-dimensional raked piles under harmonic excitation is discussed. The piles have been represented by a three-dimensional frame structure and the soil has been represented by a boundary element discretization scheme. A computer program has been written which carries out this analysis and produces a group stiffness matrix that can be included as a f...
متن کاملDirect Spherical Harmonic Transform of a Triangulated Mesh
Spherical harmonic transform plays an important role in research in shape description. Current computation methods involve expensive voxelization, and are prone to numerical errors associated with the size of the voxels. This paper describes a fast and accurate technique for computing spherical harmonic coe cients directly from the description of the mesh.
متن کاملCoupled quasi-harmonic bases
The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases...
متن کاملSoftware Tools for Record Fault Analysis in Power Systems
We have available, in today’s application of microprocessor based relays and digital fault recorders, record analysis software. This software shows graphical and numerical information along with powerful tools that are easy to use. These are applied by relay protection engineers, to analyze the records and provide a more efficient analysis for simple and complex cases. These tools also provide ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011