In speech processing, the speech is often considered stationary within segments of 20-30 ms even though it is well known not to be true. In this paper, we take the non-stationarity of voiced speech into account by using a linear chirp model to describe the speech signal. We propose a maximum likelihood estimator of the fundamental frequency and chirp rate of this model, and show that it reaches the Cramer-Rao lower bound. Since the speech varies over time, a fixed segment length is not optimal, and we propose making a segmentation of the signal based on the maximum a posteriori (MAP) criterion. Using this segmentation method, the segments are on average longer for the chirp model compared to the traditional harmonic model. For the signal under test, the average segment length is 24.4 ms and 17.1 ms for the chirp model and traditional harmonic model, respectively. This suggests a better fit of the chirp model than the harmonic model to the speech signal. The methods are based on an assumption of white Gaussian noise, and, therefore, two prewhitening filters are also proposed.

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.

In this paper, the important problem of single-channel noise reduction is treated from a new perspective. The problem is posed as a filtering problem based on joint diagonalization of the covariance matrices of the desired and noise signals. More specifically, the eigenvectors from the joint diagonalization corresponding to the least significant eigenvalues are used to form a filter, which effectively estimates the noise when applied to the observed signal. This estimate is then subtracted from the observed signal to form an estimate of the desired signal, i.e., the speech signal. In doing this, we consider two cases, where, respectively, no distortion and distortion are incurred on the desired signal. The former can be achieved when the covariance matrix of the desired signal is rank deficient, which is the case, for example, for voiced speech. In the latter case, the covariance matrix of the desired signal is full rank, as is the case, for example, in unvoiced speech. Here, the amount of distortion incurred is controlled via a simple, integer parameter, and the more distortion allowed, the higher the output signal-to-noise ratio (SNR). Simulations demonstrate the properties of the two solutions. In the distortionless case, the proposed filter achieves only a slightly worse output SNR, compared to the Wiener filter, along with no signal distortion. Moreover, when distortion is allowed, it is possible to achieve higher output SNRs compared to the Wiener filter. Alternatively, when a lower output SNR is accepted, a filter with less signal distortion than the Wiener filter can be constructed.

A new filter design based on joint diagonalization of the clean speech and noise covariance matrices is proposed. First, an estimate of the noise is found by filtering the observed signal. The filter for this is generated by a weighted sum of the eigenvectors from the joint diagonalization. Second, an estimate of the desired signal is found by subtraction of the noise estimate from the observed signal. The filter can be designed to obtain a desired trade-off between noise reduction and signal distortion, depending on the number of eigenvectors included in the filter design. This is explored through simulations using a speech signal corrupted by car noise, and the results confirm that the output signal-to-noise ratio and speech distortion index both increase when more eigenvectors are included in the filter design.

In some situations, such as open office spaces, speech can play the role of an unwanted and disturbing source of noise, and ANC headphones or earbuds might help to solve this problem. However, ANC in modern headphones is often based on a pre-calculated fixedfilter for practical reasons, like stability and cost. Moreover, in some cases the optimal filter is non-causal, which cannot be realized with such a filter, and ANC attenuation performance will be significantly decreased. In this paper we propose to solve the causality problem in feedforward fixed-filter ANC systems by integrating a long-term linear prediction filter to predict the incoming disturbance, here speech, by the same amount of samples ahead in time, as the non-causal delay. The proposed ANC system outperforms conventional adaptive feedforward ANC systems in terms of computational complexity, showing comparable or better results on voiced speech attenuation at non-causal delays from 4 to 18 samples (0.5 to 2.25 ms) at a sampling frequency of 8 kHz.