Note thatR i is an even function of i, i. An autocorrelation matrix is a symmetricToeplitz matrix. A Toeplitz matrix is one where allthe elements along each diagonal are equal . In practice, the signal s, is known over only a finite interval,or we are interested in ,the signal over only a finite interval. One popular method is to multiply the signal s, by a windowfunction w, to obtain another signal s; that is zero outsidesomeinterval O.
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Sign In. Linear prediction: A tutorial review Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals. The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal. In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum.
The major part of the paper is devoted to all-pole models. The model parameters are obtained by a least squares analysis in the time domain. Two methods result, depending on whether the signal is assumed to be stationary or nonstationary. The same results are then derived in the frequency domain. The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra.
This also leads to a discussion of the advantages and disadvantages of the least squares error criterion. A spectral interpretation is given to the normalized minimum prediction error. Applications of the normalized error are given, including the determination of an "optimal" number of poles. The use of linear prediction in data compression is reviewed. For purposes of transmission, particular attention is given to the quantization and encoding of the reflection or partial correlation coefficients.
Finally, a brief introduction to pole-zero modeling is given. Article :. Date of Publication: April Sponsored by: IEEE. Need Help?
linear Prediction: A Tutorial Review
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: This paper gives an exposition of linear prediction in the analysis of discrete signals.
Linear prediction: A tutorial review