We have a periodic input signal with the period of T=12.
Can we have a periodic output signal with the period of T=3 in a LTI system?
Can we have a periodic output signal with the period of T=3 in a LTI system?
Hello there,Your question is equivalent to asking if it is possible for an LTI system to have an output at four times the frequency of the forcing function. The order of the LTI is important and you have not specified it in this context.
The following is from the wikipedia article
Because sinusoids are a sum of complex exponentials with complex-conjugate frequencies, if the input to the system is a sinusoid, then the output of the system will also be a sinusoid, perhaps with a different amplitude and a different phase, but always with the same frequency upon reaching steady-state. LTI systems cannot produce frequency components that are not in the input.
Systems with non-linear elements do create new frequencies that are not in the input. For example a multiplier will create new frequencies at the sum and difference of the two input frequencies.
Given that it only has to be periodic, we could imagine choosing two frequencies one 100Hz and the other 400Hz where the 400Hz signal is of lower amplitude than the 100Hz. This kind of input would look like it had a period of 1/100 seconds. We could then imagine a high pass filter or maybe a band pass filter that attenuates the 100Hz sine a lot but doesnt affect the 400Hz sine too much. We'd then see something that looked more like it had a period of 1/400 seconds.We have a periodic input signal with the period of T=12.
Can we have a periodic output signal with the period of T=3 in a LTI system?
I already agreed that any sinusoidal signal as input will only produce the same frequency. Combinations of sinusoids could be different because we are looking only at the period of a signal that is not sinusoidal.We have a periodic input signal with the period of T=12.
Can we have a periodic output signal with the period of T=3 in a LTI system?
For some reason you want to over specify the original question where we have to impose some previously unmentioned criterion on the question result. Are we not allowed to reply to the EXACT question being asked without adding more criteria?Challenge:
Show me an LTI with any combination of input sinusoids that produces new frequencies.
Part 1: "We have a periodic input signal with the period of T=12"We have a periodic input signal with the period of T=12.
Can we have a periodic output signal with the period of T=3 in a LTI system?
by Duane Benson
by Duane Benson