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 >

Last year i got a very different mathematical book as a gift. A comic novel from Doxiadis, Papadimitriou and Papadatos: Logicomix. It is easy to read and provides some insight of the mathematical quest in the area of logic of the last century. You’ll meet people like Bertrand Russel, David Hilbert, Gödel and many more outstanding persons. Some work results of the main actors are presented in that way that is accessible for a wide audience – according to the rules used in popular science media. So even mathematical illiterate persons may enjoy the comic and due to the very nice illustrations i think even kids could enjoy it. The “showdown” is Gödel’s incompleteness theorem and i enjoyed the way the result was presented. The authors admit at the end of the book that the storyline is only loosely based on historical facts but actually this doesn’t reduce the value of the novel. Reading this comic was a nice way to relax during a cold winter’s day. Give it a try !

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 >

In [1, p. 62 exercise 3.16] we are asked to show that the random process

(1)

, where is uniformly distributed on , is WSS by finding its mean and ACF. Using the same assumptions we are asked to repeat the exercise for a single complex sinusoid

(2)

read the conclusion >

In [1, p. 62 exercise 3.15] it is requested to verify the ACF and PSD relationships given in [1, p. 53 eq. (3.50)] and [1, p. 54 eq. (3.51)]. read the conclusion >