"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

24 Jun

In [1, p. 94 exercise 4.2] we are asked to consider the estimator

where

for the process of Problem 4.1. We are informed that this estimator may be viewed as an averaged periodogram. In this point of view the data record is sectioned into blocks (in this case, of length 1) and the periodograms for each block are averaged. We are asked to find the mean and variance of and compare the result to that obtained in [2]. read the conclusion >

(1) |

where

(2) |

for the process of Problem 4.1. We are informed that this estimator may be viewed as an averaged periodogram. In this point of view the data record is sectioned into blocks (in this case, of length 1) and the periodograms for each block are averaged. We are asked to find the mean and variance of and compare the result to that obtained in [2]. read the conclusion >

1 Feb

In problem [1, p. 94 exercise 4.1] we will show that the periodogram is an inconsistent estimator by examining the estimator at , or

If is real white Gaussian noise process with PSD

we are asked to find the mean an variance of . We are asked if the variance converge to zero as . The hint provided within the exercise is to note that

where the quantiiy inside the parenthesis is read the conclusion >

(1) |

If is real white Gaussian noise process with PSD

(2) |

we are asked to find the mean an variance of . We are asked if the variance converge to zero as . The hint provided within the exercise is to note that

(3) |

where the quantiiy inside the parenthesis is read the conclusion >

17 Mai

In [1, p. 62 exercise 3.19] we are asked to find for the multiple sinusoidal process

the ensemble ACF and the temporal ACF as , where the ‘s are all uniformly distributed random variables on and independent of each other. We are also asked to determine if this random process is autocorrelation ergodic. read the conclusion >

the ensemble ACF and the temporal ACF as , where the ‘s are all uniformly distributed random variables on and independent of each other. We are also asked to determine if this random process is autocorrelation ergodic. read the conclusion >

24 Aug

In [1, p. 62 exercise 3.18] we are asked to find the temporal autocorrelation function for the real sinusoidal random process of Problem [1, p. 62 exercise 3.16]:

as . As a second step we are asked to determine if the random process autocorrelation ergodic. read the conclusion >

as . As a second step we are asked to determine if the random process autocorrelation ergodic. read the conclusion >

19 Apr

In [1, p. 62 exercise 3.17] we are asked to verify that the variance of the sample mean estimator for the mean of a real WSS random process

is given by [1, eq. (3.60), p. 58]. For the case when is real white noise we are asked to what the variance expression does reduce to. A hint that is given is to use the relationship from [1, eq. (3.64), p. 59]. read the conclusion >

is given by [1, eq. (3.60), p. 58]. For the case when is real white noise we are asked to what the variance expression does reduce to. A hint that is given is to use the relationship from [1, eq. (3.64), p. 59]. read the conclusion >