I am learning about digital filters, for example a lowpass butterworth filter.
In many languages, the implmentation requires specification of the order of the filter, which I believe is the number of terms in the closed form equation that generates each filtered sample, given the original samples and previously generated samples.
What I haven't been able to find (at a sufficiently ELI5 level) is how the order affects the frequency and phase response of the filter.
Does a higher order simply mean a better approximation to the optimal filter with (cutoff, stopband) ? Do higher orders mean different or less severe phase differences?
Finally, I'd assume that it affects performance somewhat as well.