椭圆三角函数及其在波形发生器中的应用

对普通三角函数进行了推广，给出了椭圆三角函数的定义，指出椭圆三角函数是周期函数，存在最大值和最小值，并在定义域内连续可导．对椭圆正弦函数进行了一系列仿真研究，结果表明，椭圆正弦函数可作为波形发生器的发生函数，可产生方波、普通正弦波、脉冲波、处于普通正弦波和方波之间的波形、处于普通正弦波和脉冲波之间的各种波形，且函数形式是一致的，波形的幅值、频率、初始相位都易于调整．这种波形发生函数能方便地进行数学处理与分析，波形发生原理能应用于各类相关波形发生场合．

Elliptical Triangle Functions and Their Application to Waveform Generators

The definition of elliptical triangle functions is given and ordinary triangle functions are generalized. It is pointed out that elliptical triangle functions are periodical with maximum and minimum values, and continuously derivable in the domain of definition. A series of simulations are carried out for elliptical sinusoidal functions. The results show that the elliptical sinusoidal function can be used as a generating function of waveform generator which can produce square waves, ordinary sine waves, pulse waves, and various waves between ordinary sine waves and square waves or between ordinary sine waves and pulse waves. Moreover, the form of the functions is uniform with amplitude, frequency, and original phrase that are easy to be adjusted. This generating function of waveform is convenient for mathematical treatment and analysis. The proposed principle of generating waveform can be applied to the cases that are related to all kinds of wave generation.