How to find the relative bandwidth /frequency of a aperiodic signal?
There are various definitions used for effective bandwidth. What is used depends largely on what is considered good enough for a particular application. One is to use a frequency spectrum which contains 99% of the total signal energy. This an arbitrary choice that is often used for analog FM radio signals.
If you simply want to calculate the content of a signal at a given frequency though, and you have the signal's spectrum and the transfer function you can just multiply the two and substitute the frequency of interest.