I want to film a moving car with a rolling circumference: 190,5 cm and wheel circumference: 60 cm and 5 spokes.
I record with 24Hz. What can be the maximal speed of the car to avoid aliasing?
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1$\begingroup$ Your question is ambiguous in two details: First what's the rolling circumference and its importance here? Second what do you exactly consider as aliasing ? A wheel that rotates back? or a wheel that seems rotating slower than it actually is doing? $\endgroup$– Fat32Nov 10, 2017 at 19:46
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1 Answer
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Let's say $\omega_w$ is wheel rotational speed, $v$ is car speed, $r = 0.3m$ ($2\pi \cdot 0.3 = 1.88m = $ rolling circumference?) is the radius of the wheel and $f_s = 24Hz$ is the sampling frequency.
Then you need to sample an event with a period of $5\omega_w$ (stokes are indistinguishable from one another). Thus, $f_{max} = \frac{5\omega}{2\pi}$.
Then, by Nyquist:
\begin{equation} f_s \gt 2f_{max} = \frac{2 \cdot 5\omega_w}{2\pi} = 5 \cdot \frac{v}{r \cdot \pi} \end{equation}
Therefore:
\begin{equation} v \lt \frac{fs \cdot r \cdot \pi}{5} = \frac{24 \cdot 0.3 \cdot \pi}{5} \approx 4.52 m/s \approx 16.28 km/h \end{equation}
