The problem of noise reduction has attracted a considerable amount of research attention over the past several decades. Among the numerous techniques that were developed, the optimal Wiener filter can be considered as one of the most fundamental noise reduction approaches, which has been delineated in different forms and adopted in various applications. Although it is not a secret that the Wiener filter may cause some detrimental effects to the speech signal (appreciable or even significant degradation in quality or intelligibility), few efforts have been reported to show the inherent relationship between noise reduction and speech distortion. By defining a speech-distortion index to measure the degree to which the speech signal is deformed and two noise-reduction factors to quantify the amount of noise being attenuated, this paper studies the quantitative performance behavior of the Wiener filter in the context of noise reduction. We show that in the single-channel case the a posteriori signal-to-noise ratio (SNR) (defined after the Wiener filter) is greater than or equal to the a priori SNR (defined before the Wiener filter), indicating that the Wiener filter is always able to achieve noise reduction. However, the amount of noise reduction is in general proportional to the amount of speech degradation. This may seem discouraging as we always expect an algorithm to have maximal noise reduction without much speech distortion. Fortunately, we show that speech distortion can be better managed in three different ways. If we have some a priori knowledge (such as the linear prediction coefficients) of the clean speech signal, this a priori knowledge can be exploited to achieve noise reduction while maintaining a low level of speech distortion. When no a priori knowledge is available, we can still achieve a better control of noise reduction and speech distortion by properly manipulating the Wiener filter, resulting in a suboptimal Wiener filter. In case that we have multiple microphone sensors, the multiple observations of the speech signal can be used to reduce noise with less or even no speech distortion

A linear-correction least-squares estimation procedure is proposed for the source localization problem under an additive measurement error model. The method, which can be easily implemented in a real-time system with moderate computational complexity, yields an efficient source location estimator without assuming a priori knowledge of noise distribution. Alternative existing estimators, including likelihood-based, spherical intersection, spherical interpolation, and quadratic-correction least-squares estimators, are reviewed and comparisons of their complexity, estimation consistency and efficiency against the Cramer-Rao lower bound are made. Numerical studies demonstrate that the proposed estimator performs better under many practical situations.

The performance of the recursive least-squares (RLS) algorithm is governed by the forgetting factor. This parameter leads to a compromise between (1) the tracking capabilities and (2) the misadjustment and stability. In this letter, a variable forgetting factor RLS (VFF-RLS) algorithm is proposed for system identification. In general, the output of the unknown system is corrupted by a noise-like signal. This signal should be recovered in the error signal of the adaptive filter after this one converges to the true solution. This condition is used to control the value of the forgetting factor. The simulation results indicate the good performance and the robustness of the proposed algorithm.

The aim of a variable step size normalized least-mean-square (VSS-NLMS) algorithm is to try to solve the conflicting requirement of fast convergence and low misadjustment of the NLMS algorithm. Numerous VSS-NLMS algorithms can be found in the literature with a common point for most of them: they may not work very reliably since they depend on several parameters that are not simple to tune in practice. The objective of this letter is twofold. First, we explain a simple and elegant way to derive VSS-NLMS-type algorithms. Second, a new nonparametric VSS-NLMS is proposed that is easy to control and gives good performances in the context of acoustic echo cancellation

Several contributions have been made so far to develop optimal multichannel linear filtering approaches and show their ability to reduce the acoustic noise. However, there has not been a clear unifying theoretical analysis of their performance in terms of both noise reduction and speech distortion. To fill this gap, we analyze the frequency-domain (non-causal) multichannel linear filtering for noise reduction in this paper. For completeness, we consider the noise reduction constrained optimization problem that leads to the parameterized multichannel non-causal Wiener filter (PMWF). Our contribution is fivefold. First, we formally show that the minimum variance distortionless response (MVDR) filter is a particular case of the PMWF by properly formulating the constrained optimization problem of noise reduction. Second, we propose new simplified expressions for the PMWF, the MVDR, and the generalized sidelobe canceller (GSC) that depend on the signals' statistics only. In contrast to earlier works, these expressions are explicitly independent of the channel transfer function ratios. Third, we quantify the theoretical gains and losses in terms of speech distortion and noise reduction when using the PWMF by establishing new simplified closed-form expressions for three performance measures, namely, the signal distortion index, the noise reduction factor (originally proposed in the paper titled ldquoNew insights into the noise reduction Wiener filter,rdquo by J. Chen (IEEE Transactions on Audio, Speech, and Language Processing, Vol. 15, no. 4, pp. 1218-1234, Jul. 2006) to analyze the single channel time-domain Wiener filter), and the output signal-to-noise ratio (SNR). Fourth, we analyze the effects of coherent and incoherent noise in addition to the benefits of utilizing multiple microphones. Fifth, we propose a new proof for the a posteriori SNR improvement achieved by the PMWF. Finally, we provide some simulations results to corroborate the findings of this work.