# A vector Taylor series approach for environment-independent speech recognition

- 1996

#### Abstract

• Where represents the power spectrum of the degraded speech, is the power spectrum of the clean speech, is the transfer function of the linear filter, and is the power spectrum of the additive noise.) (|) (|) () Z(2 ω ω ω ω N H X + =) Z(ω) X(ω) (ω H) (ω N • In the log-Spectral domain this relation can be expressed as:) 1 log(q x n e q x z − − + + + = of in more general term:) , , (q n x f x z + = where is an unknown parameter that represents the effects of linear filtering in the log-spectra domain. • We also assume that the PDF of the log-spectra of the speech signal can be well represented by a summation of multivariate Gaussian distributions: ∑ − = Σ = 1 0 , ,) (] [) (, M k k x k x x N k P x p μ • The problem of compensation is two fold. First, the parameters , , ,and need to be determined. Second, the distribution of given the PDF of and the parameters , , and has to be computed. Because of the non-linearity of the function , both problems are non-trivial. Only for very simple expressions of the function can be computed analytically. • Furthermore, we assume that the statistics of noise can be well represented by a single Gaussian .) , (n n n N Σ μ q q n μ n μ n Σ n Σ z x) , , (q x n f) , , (q x n f) (z p But function like is not possible to compute analytically.) 1 log(q x n e − − +) (z p • While could be computed by Monte-carlo methods, this approach is computationally expensive and requires previous knowledge of the parameters , and. VTS provides a framework that enables an analytical solution to both problems.) (z p q n μ n Σ DESCRIPTION OF THE VTS ALGORITHMS • The key of the new VTS algorithm is to approximate the generic vector function with a vector Taylor series approximation: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 q q q n x f dq d n n q n x f dn d x x q n x f dx d q n x f …

**DOI:**10.1109/ICASSP.1996.543225