I am measuring some property of a material that depends on the rotation angle of the material. Let the property be $f(\theta)$ , where $\theta$ is the rotation angle. From physics, we know that $f(\theta)$ is a periodic function with a period of $\frac{\pi}{2}$. However, since our measurement process is slow and discrete, we can take only a few measurement data. Our goal is to express the function $f(\theta)$ as a Fourier series of 3 harmonics. My question is how many equally spaced data points are needed to specify a unique three harmonic Fourier series ?
Thank you.
The Nyquist–Shannon sampling theorem states that, considering uniform sampling, the sample rate must be at least twice the bandwidth of the signal. In your question, the 3rd harmonic has a period of $\frac {\pi}{6}$, which means your sampling period should be less than or equal to $\frac {\pi}{12}$.