system response question

[fanshuo]

If a system has a pole in frequency domain,say the pole lies in f1
the input is a sinewave with frequency f2
the output will have a frequency component at frequency abs(f1-f2)
how to prove this?

Thanks!

 

[Ghitani]

I think that his system is a simple first order LPF and the output must have the same input frequency

 

[fanshuo]

it is not exactly a low pass filter
I do find the f1-f2 term in simulation

or my question could be asked in the following way:

if the system response at f1 is infinite and at frequency other than f1 is 0
the input is at frequency f2,with finite amplitude(say 1)
the output has a component at f1-f2? why?

 

[angelote]

Find out about convolution in "Communication Systems" of "A. Bruce Carlson".

 

[fanshuo]

Well, I found what my mistake is.
Thanks for attention