Dev records a 14 Hz hum at 20 readings each second…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Dev records a Hz hum at readings each second. What is the highest frequency his readings can show correctly? What frequency will his FFT show for the hum?
Need a reminder? The key ideaShow
np.fft.rfftfreq(n, d) gives frequencies apart, and the tallest bar of np.abs(np.fft.rfft(y)) is the main frequency. A reading rate can show frequencies up to ; above that a wave aliases to . curve_fit returns popt and pcov, and the errors are np.sqrt(np.diag(pcov)).
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The limit. Half of readings each second is Hz.
Step 2. The hum. Hz is above Hz, so the readings cannot show it.
Step 3. The fold. It appears at Hz.
Step 4. The cure. Read faster than times each second, and the FFT shows Hz.
Answer: the limit is Hz, and the FFT shows a false Hz.
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