Enhancement and Noise Statistics Estimation for Non-Stationary Voiced Speech

Abstract

In this paper, single channel speech enhancement in the time domain is considered. We address the problem of modelling non-stationary speech by describing the voiced speech parts by a harmonic linear chirp model instead of using the traditional harmonic model. This means that the speech signal is not assumed stationary, instead the fundamental frequency can vary linearly within each frame. The linearly constrained minimum variance (LCMV) filter and the amplitude and phase estimation (APES) filter are derived in this framework and compared to the harmonic versions of the same filters. It is shown through simulations on synthetic and speech signals, that the chirp versions of the filters perform better than their harmonic counterparts in terms of output signal-to-noise ratio (SNR) and signal reduction factor. For synthetic signals, the output SNR for the harmonic chirp APES based filter is increased 3 dB compared to the harmonic APES based filter at an input SNR of 10 dB, and at the same time the signal reduction factor is decreased. For speech signals, the increase is 1.5 dB along with a decrease in the signal reduction factor of 0.7. As an implicit part of the APES filter, a noise covariance matrix estimate is obtained. We suggest using this estimate in combination with other filters such as the Wiener filter. The performance of the Wiener filter and LCMV filter are compared using the APES noise covariance matrix estimate and a power spectral density (PSD) based noise covariance matrix estimate. It is shown that the APES covariance matrix works well in combination with the Wiener filter, and the PSD based covariance matrix works well in combination with the LCMV filter.

Choice of Sampling Interval and Extent for Finite-Energy Fields

“…where (27) is due to the Cauchy-Schwarz inequality. Then, we make use of Nyquist's sampling theorem to expressF Δ μ aŝ…”

“…holds true for all k ∈ N, we conclude (31) from the dominated convergence theorem. The inequality (27) and the equality (31) suggest that the aliasing error…”

“…As for the study of non-stationary signals, we can only mention a small sample of recent papers [23]- [27]. Reference [28] is a special issue dedicated to the subject.…”

Fast harmonic chirp summation

“…The HCM has only very recently been used in [8] as an alternative to modelling non-stationary speech using amplitude modulation models [9]. The HCM was also used in the context of speech processing in [10,11], but was considered in a more general framework in [12,13] in which animal sound signals were analysed. In all of these papers, the complex-valued HCM was used although we know of no application where such signals naturally occur.…”

Harmonic and non-Harmonic Based Noisy Reverberant Speech Enhancement in Time Domain

“…In the literature, speech enhancement approaches are designed to mainly improve the speech quality in adverse conditions [19] [20][21] [22]. These solutions identify the distortion components based on temporal and spectral estimators [23] or using decomposition techniques such as the EMD (Empirical Mode Decomposition) [24]. The OMLSA (Optimally-Modified Log-Spectral Amplitude) [19] adopts an acoustic noise estimator to access the spectral noise power and reconstruct the speech signal based on the minimization of the logspectral mean square error.…”