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- probabilistic methods of signal and system analysis

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Exercise 6-4.1 An ergodic random process has an autocorrelation function of the form Rx (r) = -10e-21rl a) Over what range of r-values must the autocorrelation function of this process be estimated in order to include all values of Rx<. r) greater...

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Exercise 6-3.2 For each of the following functions of r, determine the largest value of the constant A for which the function could be a valid autocorrelation function: a) e-41TI _ Ae-21TI b) e-IT+AI c) 10 cos (2r) - A cos (r)

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Exercise 6-3.1 a) An ergodic random process has an autocorrelation function of the form Rx(•) = 9e-4ITI + 16 cos 10-r: + 16 Find the mean-square value, mean value, and variance of this process. b) An ergodic random process has an autocorrelation func...

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Exercise 6-2.2 x(t) 0 -A A sample function from a stationary random process is shown above. The quantity t0 is a random variable that is uniformly distributed from O to ta and the pulse ampl itudes are ±A with equal-probability and are independent fr...

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Exercise 6-2.1 A speech waveform is sampled 4000 times a second and each sample is quantized into 256 ampl itude levels. The resulting ampl itude levels are represented by a binary voltage having values of ±5. Assuming that successive binary symbols ...

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Exercise 6-1 .2 Define a random variable Z(t) as Z(t) = X(t) + X(t + r1) where X(t) is a sample function from a stationary random process whose autocorrelation function is Rx (r) =- exp(- r 2 ) Write an expression for the autocorrelation function of ...

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Exercise 6-1 .1 A random process has sample functions of the form X(t) =A =0 0 :::: t :::: 1 elsewhere where A is a random variable that is uniformly distributed from 0 to 1 0. Using the basic definition of the autocorrelation function as given by Eq...

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5-6.3 Using a random number generator generate 200 random numbers having a Gaussian distribution with mean of 10 and standard deviation of 5. From these numbers a) estimate the mean of the process b) estimate the variance of the process c) estimate t...

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5-6.2 Estimate the variance of the process in Problem 5-6. 1.

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5-6.1 A stationary random process is sampled at time instants separated by 0.01 seconds. The resulting sample values are tabulated below. x(i) . x(i) x(i) 0 0. 19 7 -1.24 14 1.45 1 0.29 8 -1 .88 15 -0.82 2 1.44 9 -0.31 16 -0.25 3 0.83 10 1.18 17 0.23...

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