Jun 9, 2016 · I am reading "space filling curve" by Hans Sagan. On page 17, on equation (2.3.11) in the equation, a function sgn is used.

知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业、友善的社区氛围、独特的产品机制以及结构化和易获得的优质内容，聚集了中文互联网科技、商业、 …

sgn函数 阶跃函数，数学上的符号函数或者计算机语言中的返回函数。 Sgn 函数 返回一个 Variant (Integer)，指出参数的正负号。

Sep 17, 2017 · Considering derivative of discontinuity as del(x). Derivative of sgn(x) would be 2*del(x), as there exist a discontinuity at x=0 and a change in step by 2 units (from -1 to +1). Note : This method is being used in mathematical modeling of signals. Where del(t) is an unit impluse function. And sgn is made up of two step functions.

$$\textrm{sgn}(\sigma) = (-1)^{\sum_{0 \le i<j<n} (\sigma_i>\sigma_j)}$$ I.e., the sign is negative iff there are an odd number of misordered pairs of indices. This algorithm also works if we're interested in the permutation defined by an unsorted list of integers where the cycle structure can't be determined in linear time.

Mar 11, 2021 · The signum function is defined as a piecewise function: $\\operatorname{sgn} (x)=\\left\\{ \\begin{matrix} 1,x&gt;0 \\\\ 0,x=0 \\\\ -1,x&lt;0 \\\\ \\end{matrix ...

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

如果利用卷积定理容易看出这个问题等价于去计算 F(w)=sgn(w)*1 ，通常理解下常数与函数卷积将得到原函数的无穷积分值结果为常数函数（此处应理解为柯西主值）故结果为零对应的时域也为零函数，然而我们考虑足够光滑的幂函数 t^k(k\in N) 作为测试函数与 \frac{1}{t}\delta(t) 作内积，不难看出 k=0 时柯 ...

Echoing @Omnonmnomnm's point: the notion of "integral" in Fourier transforms very often needs to be an "extension by continuity" (in a topology that may vary, depending on context), so is in any case absolutely not any kind of Riemann, Lebesgue, or other "integral".

Now that you have established this well definedness property of sgn the problem becomes much easier. You can consider the 4 possible cases when l and k are even and odd respectively. You can consider the 4 possible cases when l and k are even and odd respectively.