对一类吉布斯现象解释方法的改进

The Improvement of the Method about Explanation of Gibbs Phenomena

针对方波函数的傅立叶级数的部分和,指出现有表达式存在的不足。给出了新的方波函数傅立叶级数前L次谐波之和的表达式。在此基础上对吉布斯现象进行了解释。用新的方法推导出傅立叶级数的部分和极值点的计算式。

For the partial sum of Fourier series of square wave functions, the weakness of the original expression is pointed out in the paper, and a new expression of Lth partial sum of Fourier series is given. Gibbs phenomenon is explained based on the above, and formulas for calculating extreme points of the partial sum of Fourier series of the square wave are inferred using a new method.