Formulate this process in state-space form

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Question: Moving Average. Suppose two initial numbers are given and successive numbers are computed as the average of last two. For example, with 1 and 3, we generate the sequence

1, 3, 2, 2½, 2¼,......

Note that the sequence seems to be converging, but not to the average of the original two numbers (which is 2).

(a) Formulate this process in state-space form.

(b) The system matrix A you obtained should be positive but not strictly positive. What is the Frobenius-Perron eigenvalue λ0?

(d) What are the right and left eigenvectors corresponding to λ0?

(e) What is the general formula for the limiting value of a sequence of this kind, expressed in terms of Its first two terms? For the example given, what is the limiting value?

(f) Now generalize to an nth-order average. That is, n initial numbers are given and successive numbers are the averages of the last n numbers. What is the formula for the limit?

Reference no: EM131466692

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