Further derivations of statistical measures in the cepstrum (Corresp.)

Author

Hassab, Joseph C.

Volume

23

Issue

4

fYear

1977

fDate

7/1/1977 12:00:00 AM

Firstpage

540

Lastpage

544

Abstract

Expanded statistical measures in the cepstrum are obtained when estimating the time delay $\\tau$ between the wavelets of a composite signal embedded in noise. Previous considerations have been limited to physical instances where the modulus $a$ and the ratio of signal to noise spectra $\\Phi _{y}/ \\Phi _{n}$ yield values for $x = (1 +a^{2}) \\Phi _{y}/ \\Phi _{n}$ and/or $\\gamma = 2|a| / (1 + a^{2})$ much less than one. The physical parameters, $a, \\Phi _{y}$ , and $\\Phi _{n}$ are allowed to vary throughout the spectrum, thus introducing new elements to the analysis. The required statistical measures are derived for the complete series of cross-terms, for a higher order perturbation in the modulation term, and for its logarithmically generated harmonics. Under these open conditions, the explicit behavior of the additional statistical measures are delineated as a function of the modulus $a$ and the ratio of signal to noise spectra. The effect of the interfering harmonics with the modulation term is assessed for signal and noise with exponential autocorrelation functions.

Keywords

Cepstrum methods; Delay estimation; Signal resolution; Autocorrelation; Cepstrum; Delay effects; Delay estimation; Diffraction; Equations; Noise measurement; Probability; Signal to noise ratio; Time measurement;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1977.1055725

Filename

1055725