/en/tags/sampling-theorem/Recent content in Sampling Theorem on Mi&Bee BlogHugo -- gohugo.ioen蓝宝石的傻话Mon, 04 May 2026 10:00:00 +0800/en/posts/physical-world/acoustics-dsp-basics/Mon, 04 May 2026 10:00:00 +0800/en/posts/physical-world/acoustics-dsp-basics/<h2 id="destructive-interference">Destructive Interference</h2> <p>Active noise cancellation (ANC) builds on a simple physical principle: destructive interference. Two sound waves of the same frequency and opposite phase cancel each other out.</p> <p>The original noise signal:</p> <p>$$ p_n(t) = A \cos(2\pi ft + \phi) $$</p> <p>The anti-noise generated by the ANC system:</p> <p>$$ p_c(t) = -A \cos(2\pi ft + \phi) = A \cos(2\pi ft + \phi + \pi) $$</p> <p>Superposition:</p> <p>$$ p_{\text{total}} = p_n(t) + p_c(t) = 0 $$</p>