A Linear Problem

For a given system,

$ e^{2jt} $ -> $ te^{-2jt} $

and

$ e^{-2jt} $ -> $ te^{2jt} $

What is the system’s response to $ cos(2t) $?


Answer

As a general answer, this system, for any input, multiplies the input by t and negates the independent variable. Or:

$ x(t) $ -> $ tx(-t) $

So, the system's response to $ cos(2t) $ is:

$ cos(2t) $ -> $ tcos(-2t) $

but, because cosine is an even function, the answer can also be written as:

$ cos(2t) $ -> $ tcos(2t) $

Alumni Liaison

Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin