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When T is very large (approaching infinity) the quanity on the left transforms to be approximately the quanity on the right.
Using the relations above, can we make an unperiodic signal such as the one given below and make it periodic by taking the limit?
note that
Using the Fourier Transform property along with then
Reordering order of integration
note that the defination of the delta function is
Using such techniquies as we did above (refered to as The Game in Signals and Systems), similar equations can be manipulated to find its output of Linear Invarient System.
THE GAME
LTI (Linear Time Invariant System)
Input LTI Output Reason
Superposition
Superposition