✳️ 离散卷积计算器Convolution Calculator
计算两个有限序列的离散线性卷积 (x * h)[n] = Σ x[k]·h[n − k]，也可选择循环卷积；给出结果序列、长度和逐项计算明细，等同于多项式乘法的系数。Compute the discrete linear convolution (x * h)[n] = Σ x[k]·h[n − k] of two finite sequences, or circular convolution, with the result, its length and a term-by-term breakdown — the same as multiplying polynomial coefficients.
使用说明与常见问题How-to & FAQ
「离散卷积计算器」是什么？What is the Convolution Calculator tool?
计算两个有限序列的离散线性卷积 (x * h)[n] = Σ x[k]·h[n − k]，也可选择循环卷积；给出结果序列、长度和逐项计算明细，等同于多项式乘法的系数。Compute the discrete linear convolution (x * h)[n] = Σ x[k]·h[n − k] of two finite sequences, or circular convolution, with the result, its length and a term-by-term breakdown — the same as multiplying polynomial coefficients.
如何使用「离散卷积计算器」？How do I use the Convolution Calculator tool?
在「离散卷积计算器」中，填写「序列 x」、「序列 h」、「类型」等参数，结果会随输入实时计算并显示在下方。In the Convolution Calculator: Fill in "Sequence x", "Sequence h", "Type"; results are recalculated instantly as you type.
线性卷积怎么算？How is linear convolution computed?
y[n] = Σₖ x[k]·h[n − k]，结果长度为 len(x) + len(h) − 1。它与两个多项式相乘时的系数完全相同。y[n] = Σₖ x[k]·h[n − k], with length len(x) + len(h) − 1 — exactly the coefficients you get when multiplying two polynomials.
循环卷积有什么不同？How does circular convolution differ?
循环卷积把较短的序列补零到相同长度 N，并对下标取模 N，结果长度为 N。它对应 DFT 的逐点相乘。Circular convolution zero-pads the shorter sequence to length N and wraps indices modulo N, giving a length-N result — the counterpart of point-wise multiplication of DFTs.
计算精度如何？How precise are the results?
「离散卷积计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Convolution Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「离散卷积计算器」免费吗？需要注册吗？Is the Convolution Calculator free? Do I need an account?
「离散卷积计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Convolution Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.