مرکز منطقه ای اطلاع رساني علوم و فناوري - Further derivations of statistical measures in the cepstrum (Corresp.)

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;