Convolution multiplies one function by a reflected, shifted copy of the other and integrates the product. For two unit boxes, that integral equals their overlap length, producing a triangular function.卷积将一个函数与另一个函数翻转、平移后的副本相乘,再对乘积积分。两个单位矩形的卷积就是它们的重叠长度,因此得到三角形函数。
The fixed interval is ; the moving interval is . Their highlighted intersection grows and shrinks, while the lower point records its length.固定区间为 ,移动区间为 。高亮交集先增大再缩小,下方光点记录它的长度。