What is a frequency bin? I'm doing a research on the FFT method, and a term that always comes up is "frequency bin". From what I understand, this has something to do with the band created around the frequency of a given sinusoid, but I can't really figure out how. I also figured out how to go from a given bin to its related frequency, but still no intuition on what a frequency bin is.
It's simpler than you think. When we discretize frequencies, we get frequency bins. So, when you discretize your Fourier Transform: $$e^{-j\omega} \rightarrow e^{-j{2\pi k}/{N}}$$ Our continuous frequencies become $N$ discrete bins.

This is exactly why the following is true: $$n^{th}bin = n*\dfrac{sampleFreq}{num(DFT points)}$$ Note that the FFT represents frequencies 0 to sampleFreq Hz.