Lysario – by Panagiotis Chatzichrisafis

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

Archive for the ‘Kay: Modern Spectral Estimation, Theory and Application’ Category

In [1, p. 62 exercise 3.16] we are asked to show that the random process
x[n]= A \cos(2\pi f_{0}n+\phi) (1)

, where \phi is uniformly distributed on (0,2\pi), is WSS by finding its mean and ACF. Using the same assumptions we are asked to repeat the exercise for a single complex sinusoid
x[n]=A\exp[j(2\pi f_{0}n+\phi)]. (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 >
In [1, p. 62 exercise 3.14] it is requested to proof prove that the autocorrelation matrix given by [1, eq. 3.46] is also positive semidefinite. This shall be done by usage of the definition of the semidefinite property of the ACF in [1, eq. 3.45]. read the conclusion >
In [1, p. 62 exercise 3.13] it is requested to prove that the PSD of a real WSS random process is a real even function of frequency. read the conclusion >
In [1, p. 62 exercise 3.12] we are asked to prove that for a WSS random process
r_{xx}[-k]=r^{\ast}[k]. (1)

read the conclusion >

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