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      <title>Learning Notes on DTW (Dynamic Time Warping)</title>
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      <pubDate>Tue, 23 Dec 2025 00:00:11 +0800</pubDate>
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      <description>&lt;h1 id=&#34;starting-with-an-intuitive-problem&#34;&gt;Starting with an Intuitive Problem&lt;/h1&gt;
&lt;p&gt;When processing audio, speech, or other time series data, we will almost certainly encounter this problem: if two signal segments are similar in &amp;ldquo;content,&amp;rdquo; but not consistent in the speed of time progression, can we still judge that they are similar?&lt;/p&gt;
&lt;p&gt;This problem is very common in real scenarios. For example, two people sing the same melody, but one sings faster and the other slower; students may slow down due to hesitation during sight-singing, retreat and re-sing after making mistakes, or suddenly accelerate at certain positions; the same sentence is spoken by different people with different speaking speeds and different pause patterns.
In these cases, if we rigidly require &amp;ldquo;frame 1 matches frame 1, frame 2 matches frame 2,&amp;rdquo; then almost all real samples will be simply and crudely judged as &amp;ldquo;not similar.&amp;rdquo;&lt;/p&gt;</description>
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