How to find the relative bandwidth /frequency of a aperiodic signal?

I have a transfer function with a fixed cut off frequency and I wanted to apply an input proportional to time(x= cont*time), also the condition is to have a frequency greater than the cut off frequency. Theoretically there will be infinite frequency (fourier transform is $$\K/(\omega^2)\$$). First of all I wanted to know if such a term called relative bandwidth/frequency is applicable in this scenario and if yes what is the idea behind it.

• Some questions to help us understand your question better: what do you mean by the conditions is to have a frequency greater than the cut-off frequency? Are you trying to evaluate the output of your system at a particular frequency? Apr 14 at 10:35
• yes, I want to check the output for a frequency greater than the cut off frequency. Lets assume the frequency is 5*cut_off_frequency. But with an input like this , what will be the effective bandwidth? Apr 14 at 10:50