Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving cardinal sine motivate an extension of classical Parseval formula both periodic non-periodic functions. We develop a version that is often more practical applications illustrate its use by extending recent results on integrals. Some previously known, are re-proved transparent manner new formulas for...

In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...

AMS Subject Classi cation: 20-04, 05C25, 20C30 Rockmore was supported in part by a National Science Foundation Mathematical Sciences Postdoctoral Fellowship. We study the complexity of performing Fourier analysis for the group SL2(Fq), where Fq is the finite field of q elements. Direct computation of a complete set of Fourier transforms for a complex-valued function f on SL2(Fq) requires q6 ope...

cisplatin is a common chemotherapeutic agent that used for treatment of many solid cancers. rapid identification of chemotherapy resistance is very important and may lead to effective treatment plan. spectroscopy techniques, such as infrared spectroscopy, which are sensitive to biochemical composition of samples, have shown potentials to discriminate tissues. developing in fourier transform inf...

detection & classification of power quality (pq) disturbances are the most important problems in distribution systems. in this paper, a new approach for the detection and classification of single and combined pq disturbances is proposed which utilizes fuzzy logic and particle swarm optimization (pso) algorithms. in this approach, first suitable features of the waveform of pq disturbances ar...