Spectrum estimation of HMM signal source in channel distortion and additive noise

Spectrum estimation of short-time stationary signals in the presence of channel distortion and additive noise is addressed. A maximum likelihood estimation algorithm is developed to jointly identify the degradation system and estimate short-time signal spectra. A source signal is assumed to be generated by a hidden Markov model (HMM) with state-dependent short-time spectral distributions of mixtures of Gaussian densities. The distortion channel is linear time-invariant and the noise is Gaussian. The unknown parameters of channel and noise are estimated iteratively using the EM algorithm, and the signal spectra are obtained from the posterior estimates of sufficient statistics of the source signal. Simulation results are provided at the signal-to-noise ratios (SNR) of 20 dB down to 0 dB and the proposed algorithm is shown to produce convergent estimation and significantly reduced spectral distortion