# Lesson 8 — Detection Theory

<p class="block-synopsis">Where the minimum detectable signal actually comes from — the noise floor, the detection threshold, and the <span class="math notranslate nohighlight">\(P_d/P_{fa}\)</span> tradeoff read off a ROC curve — plus the integration gain that turns a longer dwell into a longer range and closes the loop on the L3 range equation.</p>

<div class="block-toc">
  <a class="bt-card bt-reading" href="L08_DetectionTheory_Reading.html">
    <span class="bt-kind">Reading</span>
    <h4>Detection Theory</h4>
    <p>Noise floor, SNR and the threshold, the ROC curve, coherent vs non-coherent integration, and <span class="math notranslate nohighlight">\(S_{\min}\)</span> as a contract.</p>
  </a>
  <a class="bt-card bt-flashcards" href="L08_Flashcards.html">
    <span class="bt-kind">Flashcards</span>
    <h4>Review deck</h4>
    <p>Key terms and relations from the lesson, in a self-test deck.</p>
  </a>
  <a class="bt-card bt-demo" href="L08_ROCExplorer_Demo.html">
    <span class="bt-kind">Demo</span>
    <h4>ROC Explorer</h4>
    <p>Slide SNR and threshold, watch the ROC climb and the noise/signal PDFs separate, and integrate N pulses for gain.</p>
  </a>
  <a class="bt-card" href="L08_Preflight.html">
    <span class="bt-kind">Pre-flight</span>
    <h4>Pre-flight quiz</h4>
    <p>Pre-class check, due before the lesson. Counts toward your IP grade.</p>
  </a>
</div>
