Start with light you can see. Then apply the same filters to a signal like the one your magnetometer records.
Predict first. Look at the spectrum and the filter curve below. What color will the screen show?
The screen shows the color, but the spectrum is hidden. Using only filters, decide what the source is made of. Then commit to an answer and reveal.
Notes are kept only while this page stays open. Copy them to your notebook.
In Stage 12 you will ask AI to apply band-pass filters to the recording of two cantilevers. The filter does to your data exactly what the colored filter does to light: it multiplies the spectrum by a transmission curve, keeping some frequencies and reducing others. The words change; the idea does not.
| Light | Your signal | Same idea |
|---|---|---|
| Transmission T(f), 0–100 % | Gain |H(f)|, 0–1 | How much of each frequency gets through |
| Cutoff in THz (or nm) | Cutoff in Hz | Where the filter's edge sits |
| Colored glass or gel: gradual edge. Dichroic (interference) filter: sharp edge. | Low-order filter: gradual. High-order filter: sharp. | How quickly transmission drops at the edge |
| Prism or spectrometer | FFT and power spectrum | Shows which frequencies are present |
| The color your eye reports | The waveform on the time graph | A mixture whose ingredients are hard to read directly |
| Brightness on the screen | Amplitude of the filtered signal | How much power got through |
| White light | White noise | Roughly equal power at every frequency; the noise is named after the light |
One difference to keep in mind: your eye is a crude spectrometer with only three kinds of color sensor, so very different spectra can produce the same color. A time graph hides frequencies in a similar way, which is why Stage 11 turned to the FFT.
This signal is built the way your Stage 10 recording is: two damped oscillations at different frequencies added together, with optional noise and a constant baseline. Light showed you what a filter keeps. Here you also see what a filter gives back: a new time record containing only the frequencies in the pass band. Design a band around each spectral peak, keep each recovered component, and compare their sum with the original.
The controls are the same as on the light tabs. Only the units changed: hertz instead of terahertz.
Predict first. The band-pass is set around the lower peak in B. Sketch what the filtered signal will look like over the first 5 seconds. How many cycles?
Keep one recovered component from each band. Panel D appears when both are kept.
Hide the two frequencies, then find them from the spectrum and design your bands.
Notes are kept only while this page stays open. Copy them to your notebook.
filtfilt approach AI tools often use); a one-direction filter would delay the recovered signal.