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 V_n.

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

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

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

What is the impulse response fi of the combined filter?

Problem 11.2.3

The output Y_n of the smoothing filter in Example 11.5 has µ_Y = 1 and autocorrelation function

Y_n is the input to another smoothing filter with impulse response

The output of this second smoothing filter is W_n.

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

(b) What is the autocorrelation function of W_n?

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

What is the impulse response g_i of the combined filter

Example 11.5

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

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

Reference no: EM131083313

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