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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...

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    $\begingroup$ To what end do you want to use these filters? I think you'll find the answer when you simply explicitly write down why you want to use them. $\endgroup$
    – Marcus Müller
    Mar 9, 2019 at 19:04
  • $\begingroup$ I want to use the filters to get a frequency spectrum in which all amplitudes are assigned to third octave center frequencies. This would allow me to summate these amplitudes with other amplitudes that are also assigned to the third octave center frequencies. $\endgroup$
    – Larzeb
    Mar 9, 2019 at 21:24
  • $\begingroup$ sooooo do you know beforehand which filters will not contain energy or do you want to look at the output to figure what the spectrum looks like? $\endgroup$
    – Marcus Müller
    Mar 9, 2019 at 21:44
  • $\begingroup$ My current plan is to perform a fft on the time signal to know up to which frequency I will have to use filters. So yes, I know the spectrum before filtering, but I don't necessarily know if a certain filter contains a significant amount of energy. $\endgroup$
    – Larzeb
    Mar 9, 2019 at 22:10
  • $\begingroup$ well, if you don't know which filter is going to contain energy or not, you'll have to run it on the signal anyway to figure that out, right? Or am I missing something? $\endgroup$
    – Marcus Müller
    Mar 9, 2019 at 22:37

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  • $\begingroup$ Well, that escalated quickly... $\endgroup$
    – Larzeb
    Mar 11, 2019 at 14:26

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