The autocorrelation function of the output

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Reference no: EM131083313

Let the random sequence Yn in Problem 11.2.3 be the input to the differentiator with impulse response,

The output is the random sequence Vn.

(a) What is the expected value of the output µV?

(b) What is the autocorrelation function of the output RV [n]?

(c) What is the variance of the output Var[Vn]?

(d) Vn is a linear function of the original input process Xn in Example 11.5:

What is the impulse response fi of the combined filter?

Problem 11.2.3

The output Yn of the smoothing filter in Example 11.5 has µY = 1 and autocorrelation function

Yn is the input to another smoothing filter with impulse response

The output of this second smoothing filter is Wn.

(a) What is µW, the expected value of the output of the second filter?

(b) What is the autocorrelation function of Wn?

(c) What is the variance of Wn?

(d) Wn is a linear function of the original input process Xn in Example 11.5:

What is the impulse response gi of the combined filter

Example 11.5

A wide sense stationary random sequence X n with µX = 1 and autocorrelation function RX [n] is the input to the order M -1 discrete-time moving-average filter hn where

For the case M = 2, find the following properties of the output random sequence Yn: the expected value µY, the autocorrelation RY [n], and the variance Var[Yn].

Reference no: EM131083313

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