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

## Question:

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 moving average transformation M. What is the associated eigenvalue?

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**Related Book For**

## Linear Algebra And Its Applications

**ISBN:** 9781292351216

6th Global Edition

**Authors:** David Lay, Steven Lay, Judi McDonald