Patent ID: 8208666

Claim:
A method for determining unbiased signal amplitude estimates after cepstral variance modification of a discrete time domain signal, wherein cepstrally modified spectral amplitudes of the discrete time domain signal are χ-distributed with 2{tilde over (μ)} degrees of freedom, the method which comprises: determining a cepstral variance of cepstral coefficients of the discrete time domain signal prior to cepstral variance modification; determining a mean cepstral variance after cepstral variance modification of modified cepstral coefficients using the cepstral variance prior to cepstral variance modification; determining the 2{tilde over (μ)} degrees of freedom after the cepstral variance modification using the mean cepstral variance; determining a bias reduction factor with the equation r 2 = μ μ ~ ⁢ ⅇ ψ ⁡ ( μ ~ ) - ψ ⁡ ( μ ) where 2μ are the degrees of freedom of the χ-distributed spectral amplitudes of the discrete time domain signal (s(t)) and ψ ⁡ ( x ) = - 0.5772 - ∑ n = 0 ∞ ⁢ ( 1 x + n - 1 1 + n ) ; and determining the unbiased signal amplitude estimates by multiplying the cepstrally-modified spectral amplitudes with the bias reduction factor according to the equation = ; where are the unbiased signal amplitude estimates, are the cepstrally-modified spectral amplitudes, and r is the bias reduction factor.