Lysario – by Panagiotis Chatzichrisafis
"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"
Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 62 exercise 3.15
Author: Panagiotis24 Mrz
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)].
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Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 62 exercise 3.14
Author: Panagiotis4 Mrz
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].
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Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 62 exercise 3.13
Author: Panagiotis23 Feb
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.
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Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 62 exercise 3.12
Author: Panagiotis20 Feb
In [1, p. 62 exercise 3.12] we are asked to prove that for a WSS random process
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![r_{xx}[-k]=r^{\ast}[k].](https://lysario.de/wp-content/cache/tex_071339ccd44d4617847bbb3e15dcf5ba.png) | (1) | ||
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Steven M. Kay: “Modern Spectral Estimation – Theory and Applications”,p. 61 exercise 3.11
Author: Panagiotis29 Jan
In [1, p. 61 exercise 3.11] it is asked to repeat problem [1, p. 61 exercise 3.10] (see also the solution [2] ) for the general case when the predictor is given as
Furthermore we are asked to show that the optimal prediction coefficients
are found by solving [1, p. 157, eq. 6.4 ] and the minimum prediction error power is given by [1, p. 157, eq. 6.5 ].
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![\hat{x}[n]=-\sum\limits_{k=1}^{p}\alpha_{k}x[n-k].](https://lysario.de/wp-content/cache/tex_e9899bf3e42bcb01eecd9ca3794e97db.png) | (1) | ||
Furthermore we are asked to show that the optimal prediction coefficients
are found by solving [1, p. 157, eq. 6.4 ] and the minimum prediction error power is given by [1, p. 157, eq. 6.5 ].
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