# Lesson 15 Flashcards — Frequency Domain and Ideal Filters

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<summary><strong>1. What do the time domain and the frequency domain each show?</strong></summary>
<div class="card-answer"><p>The time domain plots amplitude against <em>time</em> — what an oscilloscope shows. The frequency domain plots amplitude against <em>frequency</em> — what a spectrum analyzer shows. Same signal, two views.</p></div>
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<summary><strong>2. What does a single sinusoid look like in the frequency domain?</strong></summary>
<div class="card-answer"><p>One <strong>spike</strong>, at its frequency, with height equal to its amplitude.</p></div>
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<summary><strong>3. Where does a DC component appear in a spectrum?</strong></summary>
<div class="card-answer"><p>As a spike at <span class="math notranslate nohighlight">\(f = 0\)</span>, with height equal to the DC value. Forgetting it is the classic bandwidth error.</p></div>
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<summary><strong>4. Does phase appear on a magnitude spectrum?</strong></summary>
<div class="card-answer"><p>No. Two signals differing only in phase produce identical magnitude spectra.</p></div>
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<summary><strong>5. How do you compute bandwidth?</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(BW = f_\text{high} - f_\text{low}\)</span>. If the signal has a DC component then <span class="math notranslate nohighlight">\(f_\text{low} = 0\)</span>.</p></div>
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<summary><strong>6. Name the four ideal filter types and what each passes.</strong></summary>
<div class="card-answer"><p><strong>Low-pass</strong> passes below <span class="math notranslate nohighlight">\(f_c\)</span>; <strong>high-pass</strong> passes above; <strong>band-pass</strong> passes between two cutoffs; <strong>band-stop</strong> passes everything except between them. A band-stop filter is also called a <strong>band-reject</strong> filter (BRF) — both names are used on assessments.</p></div>
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<summary><strong>7. What is a notch filter?</strong></summary>
<div class="card-answer"><p>A band-stop filter tuned very narrowly — the way you remove a single interfering tone without disturbing the rest of the signal.</p></div>
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<summary><strong>8. What does an ideal filter do to a component in its passband? Its stopband?</strong></summary>
<div class="card-answer"><p>Passband components survive at <strong>full height</strong>, unchanged. Stopband components <strong>vanish</strong> entirely. There is no partial attenuation in the ideal case.</p></div>
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<summary><strong>9. What does a high-pass filter always remove?</strong></summary>
<div class="card-answer"><p>The <strong>DC term</strong>, since DC sits at <span class="math notranslate nohighlight">\(f=0\)</span>. This is exactly how a demodulator strips the bias off a recovered message.</p></div>
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<summary><strong>10. Give four reasons to filter a signal.</strong></summary>
<div class="card-answer"><p>Select one signal and reject others; remove noise outside the band of interest; prevent aliasing before an ADC; and split a signal into bands — as a speaker crossover does.</p></div>
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