Lesson 15 Flashcards — Frequency Domain and Ideal Filters

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1. What do the time domain and the frequency domain each show?

The time domain plots amplitude against time — what an oscilloscope shows. The frequency domain plots amplitude against frequency — what a spectrum analyzer shows. Same signal, two views.

2. What does a single sinusoid look like in the frequency domain?

One spike, at its frequency, with height equal to its amplitude.

3. Where does a DC component appear in a spectrum?

As a spike at \(f = 0\), with height equal to the DC value. Forgetting it is the classic bandwidth error.

4. Does phase appear on a magnitude spectrum?

No. Two signals differing only in phase produce identical magnitude spectra.

5. How do you compute bandwidth?

\(BW = f_\text{high} - f_\text{low}\). If the signal has a DC component then \(f_\text{low} = 0\).

6. Name the four ideal filter types and what each passes.

Low-pass passes below \(f_c\); high-pass passes above; band-pass passes between two cutoffs; band-stop passes everything except between them. A band-stop filter is also called a band-reject filter (BRF) — both names are used on assessments.

7. What is a notch filter?

A band-stop filter tuned very narrowly — the way you remove a single interfering tone without disturbing the rest of the signal.

8. What does an ideal filter do to a component in its passband? Its stopband?

Passband components survive at full height, unchanged. Stopband components vanish entirely. There is no partial attenuation in the ideal case.

9. What does a high-pass filter always remove?

The DC term, since DC sits at \(f=0\). This is exactly how a demodulator strips the bias off a recovered message.

10. Give four reasons to filter a signal.

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.