构造广义自傅里叶函数的“两项积”法则

Constructing Self Fourier Functions by Two Terms of Product

在Ｃａｏｌａ给出的“四项和”的自傅里叶函数构造法中，如其发生函数ｇ（ｘ）为奇函数，将得到毫无意义的自傅里叶函数。本文给出另一种“两项积”自傅里叶函数构造法并分析其优缺点。它与Ｃａｏｌａ法互为补充。从而，不管是奇函数、偶函数还是非奇非偶函数都可以用来构造自傅里叶函数。如使用它们的组合。

The generation function g(x) has to be even with the recipe of 'four terms of sum'given by Caola to construct SFFs(Self Fourier Functions),otherwise the result function will be meaningless.A novel method to construct SFFs by “two terms of products” is suggested in this paper.It can overcome the shortcoming of Caolas recipe and is mutually complementary to Caolas recipe.Their combination can form complex better recipes for constructing SFFs.