Issue Number: Vol. 3, No. 4
Year of Publication: 2013
Page Numbers: 411-429
Authors: Claude Ziad Bayeh
Journal Name: International Journal of Digital Information and Wireless Communications (IJDIWC)
- Hong Kong


The Elliptic Jes window forms are original studies introduced by the author in Mathematics and Signal Processing in 2012. They are based on an Elliptical Trigonometry function “Ejes” in which it can produce a large number of different signals and shapes by varying only one parameter. In this paper, the developed study is the application of the Elliptical Trigonometry in signal processing in which some formulae are introduced using the function “Ejes”, these formulae has many advantages ahead the traditional window functions such as improving the convergence of the Fourier series at the discontinuity more rapidly compared to the traditional window functions, the proposed window functions are used to truncate the Fourier series with variable window shapes that keep the necessary information about the signal even after truncation. The proposed window functions are variable in form; they can take a huge number of different forms by varying only a few numbers of parameters. The proposed window functions can be used in both analog and digital design of filters. In fact, the General trigonometry and its sub-topics such as Elliptical Trigonometry can have also other applications in any scientific field that uses the trigonometry and it can improve all previous studies by replacing the traditional trigonometric functions such as cosine and sine by General trigonometric functions such as Gjes and Gmar or other functions.