⚙️ 工程
洛巴切夫斯基积分公式Lobachevsky’s integral formula
洛巴切夫斯基积分公式展示了周期为π的偶函数所具备的显著数学性质。该定理在傅里叶分析和信号处理领域具有重要且直接的应用价值。即使在 f(x) = 1 的特殊情况下，该公式依然能提供有意义的数学洞察。它是处理复杂信号周期性积分与求和问题的有力理论工具。
John
Posted on 22 June 2026 by John
Let f be an even function with period π. Then the following remarkable theorem by Lobachevsky holds.
This theorem is useful in Fourier analysis and signal processing. It’s useful to know even in the special case f(x) = 1.
For a “jinc” analog, see this paper.
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Every time I see the name Lobachevsky I think of Tom Lehrer’s song about him. You can find the words here and the audio here.
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