The observed process consisting of a sum of sinusoids and white noise is denoted by time series X…
The observed process consisting of a sum of sinusoids and white noise is denoted by time series X… | savvyessaywriters.org
The observed process consisting of a sum of sinusoids and white noise is denoted by time series Xk. The filter output Yk is expressed as
where
Show that adaptive weights to constrained adaptive problem as given in Exercise 4.15 is given by
where
and µ is positive scalar constant. (See V. V. Reddy, B. Egardt, and T. Kailath, “Least Squares Type Algorithm for adaptive Implementation of Pisarenko Harmonic Retrieval Method,” IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-30, No.3, June 1982, and P. A. Thompson, “An Adaptive Spectral Analysis Technique for Unbiased Frequency Estimation in the Presence of White noise,” 13th Asilomar Conf. on Circuits, Systems and Computers, Pacific Grove, California, Nov. 5-7, 1979.)
Exercise 4.15
Autoregressive moving average (ARMA) PSD estimation. The ARM A model is given by
where
And
It is assumed that the polynomials
have roots inside the unit circle. The ARM A model can also be written as
where
Show that
where {hi} are defined as impulse response filter function of the ARM A model (see Problem 4.9).
(c) Let us denote the z-transform of the impulse response function as
Show that
where co ≡ 1
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