Introduction to the Elliptical Trigonometry Series using two functions Absolute Elliptic Jes (AEjes) and Absolute Elliptic Mar (AEmar) of the first form

摘要

The Elliptical Trigonometry Series is an original study introduced in mathematical domain, in signal processing and in signal theory; it is a means of representing a periodic signal as a finite or infinite sum of Absolute Elliptic Jes (AEjes) and Absolute Elliptic Mar (AEmar) functions compared to cosine and sine functions in Fourier series. The Elliptical Trigonometry Series is more advanced than the Fourier series. The Fourier series is a particular case of the Elliptical Trigonometry Series when the value of AEjes is equivalent to Cosine and the value of AEmar is equivalent to Sine. The new series has many advantages ahead the Fourier series such as we can reduce the number of parameters for a periodic signal formed by the sum of AEjes and AEmar functions compared to the cosine and sine function in Fourier Series, reduce the circuit size that produce this periodic signal, and reduce the cost of circuits and many other advantages are remarked. In fact, the Elliptical Trigonometry is an original study introduced in Mathematics by the author and it is published by WSEAS journal, and it has enormous applications in mathematics, electronics, signal processing, signal theory and many others domains. This paper emphasizes the importance of this trigonometry in forming what is called the Elliptical Trigonometry Series. In fact, this new Series is introduced for electronics applications in order to reduce as possible the circuit size that form a specific signal and therefore reduce the cost, this is not the case of the Fourier series for the same produced signal. Moreover, we can form from only one circuit an infinite number of combined periodic signals which is not the case of the Fourier series in which one circuit can't produce more than one signal.