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.
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\$\begingroup\$ 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? \$\endgroup\$– jramsay42Commented Apr 14, 2021 at 10:35
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\$\begingroup\$ 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? \$\endgroup\$– Hari KrishnaCommented Apr 14, 2021 at 10:50
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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.
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\$\begingroup\$ Okay thank you, I was ambiguous about the term effective bandwidth. \$\endgroup\$ Commented Apr 14, 2021 at 11:02
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\$\begingroup\$ I have one more doubt , in this case the function is cont/w^2, at w=0 the value tend to infinity. So how can I take any percentage of area. \$\endgroup\$ Commented Apr 14, 2021 at 11:19