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Homework 3 Ben Horst: A  :: B  :: C


Answer

If the system is linear (it is) then the following should be true:

Thus, if we say

x1 = exp(2jt) and x2 = exp(-2jt)

then

y1 = t exp(-2jt) and y2 = t exp(2jt)


That means that:

x1 + x2 ->|system|-> y1 + y2


Since $ \cos(2t) = {e^{j2t} + e^{-j2t} \over 2} $

Then we can suggest that $ {1 \over 2}x1 + {1 \over 2}x2 -> |system| -> {1 \over 2}y1 + {1 \over 2}y2 $

This leads to the conclusion that the response to cos(2t) would be $ {1 \over 2}y1 + {1 \over 2}y2 $

Which, simplified, is: $ t\cos(2t) $.

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