I would like to use third octave filters on a time signal. Do I have to apply all third octave filters to a single frequency or do I only need to apply the one that has its center frequency the closest to the frequency that I am looking at?
I would like to use a simple example to make my quesion clear:
Let's say I have a basic sin signal:
signal = sin(2*pi*f*t) with f = 57Hz.
57Hz is almost right between the center frequencies of 50Hz and 63Hz, but the closest would be 63Hz. Do I apply all filters or only the one with a center frequency of 63Hz?
I am pretty sure that the answer is that I will always have to apply all filters in theory. Of course filters with much higher center frequencies will result in insignificant amplitudes...