Note #1. Discrete-Time δ [ n ] and u [ n ] Spring 2007 Definition. Unit impulse function (sample pulse). ≠ = =0 ,00 , 1 ] [ n n n A shifted impulse Definition. Unit step function. < ≥ =0 ,00 , 1 ] [ n n n u Thus, ∑ ∞ =-= +-+-+-+ =0 ] [ ... ] [ ... ] 2 [ ] 1 [ ] [ ] [ k k n k n n n n n u . Now express this sum in a more useful form. Change dummy variable. Let k n m-= , so that ∑-∞ = = n m m n u ] [ ] [ . Since the dummy variable is arbitrary, let’s change it back to k , i.e. , let m k = , and reverse the order of the summation so that
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