The shift transformation, S.({yk}) = {yk-1}, shifts each entry in the signal one position to the right. The moving average transformation,

creates a new signal by averaging two consecutive terms in the given signal. The constant signal of all ones is given by χ = {1^k} and the alternating signal by a = {(-1)^k}.

Show that a is an eigenvector of the shift transformation S. What is the associated eigenvalue?

Transcribed Image Text:

M₂({Yk }) = Yk + Yk-1 2