The harmonic function F exp(j2rvt) plays an important role in science and engineering. It has frequency v and complex amplitude F. Its real part IFIcos(2~vt + arg{F}) is a cosine function with amplitude jF( and phase arg{F}. The variable t usually represents time; the frequency v has units of cycles/s or Hz. The harmonic function is regarded as a building block from which other functions may be...

Usually we shall just call A an algebra if the field k is clear from the context. The algebra A is associative if multiplication is associative i.e. for all a, b, c ∈ A, (ab)c = a(bc), and unital if there is a multiplicative identity, i.e. an element usually denoted by 1 such that, for all a ∈ A, 1a = a1 = a. Note that, in this case, 1 = 0 ⇐⇒ A = {0}. Otherwise, the map k → A defined by t 7→ t·...

Fast Fourier Transform is one of the most important numerical algorithms in history. It has wide range of applications: audio signal processing, medical imaging, image processing, pattern recognition, computational chemistry, error correcting codes and spectral methods for PDE’s. The goal of this project is to implement an OpenCL based FFT algorithm that has comparable performance with existing...

In order to define a geometric Fourier transform, one usually works with either `-adic sheaves in characteristic p > 0 or with D-modules in characteristic 0. If one considers `-adic sheaves on the stack quotient of a vector bundle V by the homothety action of Gm, however, Laumon provides a uniform geometric construction of the Fourier transform in any characteristic. The category of sheaves on ...

nowadays with increasing use of numerous nonlinear loads, voltage and current harmonics in power systems are one of the most important problems power engineers encounter. many of these nonlinear loads, because of their dynamic natures, inject time-varying harmonics into power system. common techniques applied for harmonics measurement and assessment such as fft have significant errors in presen...

this paper describes an efficient edge-preserved regularization algorithm for downward continuation of magnetic data in detection of unexploded ordnance (uxo). the magnetic anomalies arising from multi-source uxo can overlap at a height over the ground surface, while causative sources may not be readily separated due to low level of signal-to-noise ratio of the observed data. to effectively the...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

DNA's double helix, the sunspot cycle and the sawtooth signals of electronics can be reduced mathematically to a series of undulating curves. This idea underlies a powerful analytical tool T o calcu1ate a transform, just listen. The ear automatically performs the calcu1ation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting...

In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT latti...