Why is the frequency measured in radians in filter design?

Question

This is my first time posting a question, so sorry if my articulation is not proper.

I'v just started out with FIR filter design and I see the domain being -$\pi$ to $\pi$. Now I understand that discrete frequencies repeat after an interval of 2$\pi$ but consider this. I need to design a low pass FIR filter with a cutoff frequency of 100$Hz$. How can I specify this in terms of radians? Is it using $\omega$=$2$$\pi$$f$? But that would be outside the domain. As you can see, I am very confused about this concept so any help would be appreciated.

Answer 1

The value of $2\pi$ radians corresponds to the sampling frequency. So the normalized frequency in radians is given by

$$\omega=\frac{2\pi f}{f_s}\tag{1}$$

where $f$ is the actual frequency in Hertz, and $f_s$ is the sampling frequency in Hertz.