Elliptic Jes window form 1

摘要

The Elliptic Jes window form 1 is an original study introduced by the first author in Mathematics and in Signal Processing. Similar to other windows used in signal processing such as: Hamming, Hanning, Blackman, Kaiser, Lanczos, Tukey and many other windows, the main goal of introducing the Elliptic Jes window form 1is to improve the convergence of the Fourier Series at the discontinuity. The different points between the proposed window function and the previous ones are: -The proposed window function is variable in form; it can take more than 12 different forms by varying only one parameter.-It can help the Fourier series to converge more rapidly compared to the traditional ones. -It can be used in both analog design of filters and digital design of filters. -It is used to truncate the Fourier series with a variable window shape that keep the necessary information about the signal even after truncation. In fact, the Elliptic Jes window form 1is an application of the Elliptic Trigonometry in Signal Processing. The Elliptical Trigonometry is an original study introduced also by the first author in mathematics in 2004, and it has an ultimate importance in all fields related to the Trigonometry topics such as Mathematics, Electrical engineering, Electronics, Signal Processing, Image Processing, Relativity, Physics, Chemistry, and many other domains. The Elliptical Trigonometry is the general case of the traditional trigonometry in which an Ellipse is used instead of a Circle, so the Elliptical Trigonometry functions are much more important compared to the traditional trigonometry functions. Therefore, all topics related to the traditional trigonometry will be ultimately improved by using the Elliptical Trigonometry functions including Signal Processing and Specifically the design of windows and filters. As a consequence, the Elliptic Jes window form 1 will replace all traditional window functions.