Enhancement of Periodic Signals: with Application to Speech Signals

The topic of this thesis is the enhancement of noisy, periodic signals with application to speech signals. Generally speaking, enhancement methods can be divided into signal- and noise-driven methods. In this thesis, we focus on the signal-driven approach by employing relevant signal parameters for the enhancement of periodic signals. The enhancement problem consists of two major subproblems: the estimation of relevant parameters or statistics, and the actual noise reduction of the observed signal. We consider both of these subproblems. First, we consider the problem of estimating signal parameters relevant to the enhancement of periodic signals. The fundamental frequency is one example of such a parameter. Furthermore, in multichannel scenarios, the direction-of-arrival of the periodic sources onto an array of sensors is another parameter of relevance. We propose methods for the estimation of the fundamental frequency that have benefits compared to other state-of-the-art estimation methods. For example, we consider improving the spectral resolution of existing subspace-based and optimal filtering based fundamental frequency estimators. Moreover, we propose fast implementations of the proposed optimal filtering based estimators, e.g., by exploiting matrix structures. This decreases the computational complexity by several orders of magnitude. We also consider the joint estimation of the fundamental frequency and the direction-of-arrival. Joint estimation enables us to resolve multiple periodic sources that share the same fundamental frequency and have different directions-of-arrival and vice versa. This may not be possible if the parameters are estimated separately. Moreover, we stress the importance of estimating the parameters jointly in relation to the estimation accuracy. Both optimal filtering based and nonlinear least squares based joint estimators are proposed; the former is excellent for resolving closely spaced sources, while the latter is statistically efficient. Then, we consider noise reduction methods based on the aforementioned parameter estimates. First, we propose several non-causal, time-domain filters for single-channel noise reduction. These non-causal filters can increase the noise reduction compared to their causal counterparts without increasing the distortion of the desired signal. We also show the link between some single-channel, signal- and noise-driven noise reduction filters; motivated by this, we suggest joint filtering schemes employing these two filter types for tackling the difficult problem of nonstationary noise reduction. It was shown that the suggested schemes outperform other widely used enhancement methods for nonstationary noise reduction in terms of perceptual scores. Finally, we propose an optimal filtering based method for multichannel periodic signal enhancement that is driven by fundamental frequency and direction-of-arrival estimates. This method was proven useful for enhancement of real-life, multichannel, periodic signals. In summary, the importance of joint parameter estimation is clarified by our contributions to the relatively young research topic of joint fundamental frequency and direction-of-arrival estimation of multichannel periodic signals. Joint estimation is a key to obtain robust and accurate fundamental frequency and direction-of-arrival estimators. Moreover, our contributions on noise reduction reveals the applicability of signal-driven enhancement of single-channel and multichannel periodic signals. By utilizing information about relevant signal parameters such as the fundamental frequency and the direction-of-arrival, noise reduction can be conducted without relying fully on the noise statistics. As appearing from our results, this can be exploited to obtain robust methods for nonstationary noise reduction.