Noise pollution is a major health threat to society. Active noise control systems that attenuate noise through open windows have the potential to create quieter homes while maintaining ventilation and sight. Such systems are commonly realized with closed-loop LMS algorithms. However, these algorithms require a large number of error microphones inside the room and provide only local attenuation. Using many error microphones leads to slow convergence and high computational effort, having additional disadvantages. Therefore, closed-loop active noise control algorithms are undesired for real-world application. In this study, we develop an open-loop wave-domain algorithm that converges instantaneously and operates with low computational effort. As it is open-loop, it does not require error microphones. We position a control region in the far-field that covers all directions from the aperture into the room. In the algorithm, we minimize the sound in that control region. Hence, it inherently ensures cancellation in the whole room. We derive acoustic transfer functions to obtain frequency responses of the aperture and loudspeakers. Those are used for soundfield calculation. The sum of the soundfields, from the aperture and the loudspeaker array, is then expressed in orthonormal basis functions. By minimizing this sum in least mean square sense, we can calculate the filter-weights that minimize the sound energy in the control region. Implementation of these filter-weights with block-wise processing using the Short-Time Fourier Transform generates the signals for the loudspeaker array. However, this processing induces a delay. To compensate for this algorithmic delay, two methods are compared. The first is positioning a reference microphone further in front of the aperture. The second method uses an autoregressive model for signal prediction. Both lead to a loss in attenuation performance compared to the optimal algorithm. We compare the optimal wave-domain algorithm with a LMS-based reference algorithm, as well as both the algorithmic delay compensation methods. The algorithms are tested with a sparse and grid loudspeaker array, and we use rumbler-siren, airplane, and white noise signals as incoming noise. Furthermore, we compare performance for three incident angles. Our simulation results indicate that wave-domain processing has the potential to outperform LMS-based methods in practical active noise control for apertures. More specifically, we obtain an average -10dB global reduction up to 2~kHz for all signal types with the optimal wave-domain approach. In comparison, the performance of the closed-loop algorithm ranges between -5.2 and -9.2dB, depending on the signal type. Furthermore, we indicate the limited impact of the incident angle on performance for the wave-domain algorithm. Positioning a reference microphone in front of the aperture outperforms the predictor approach in all scenarios, and its performance compares to that of the closed-loop LMS algorithms. Eventually, the absence of error microphones and inherent global control ensure that the wave-domain algorithm can be used for a practical active noise control system for apertures. Future work could improve the algorithm by reducing loss of performance with small window-sizes due to time-delay wrapping in the block-wise processing. Furthermore, a natural continuation of this study is to develop and test the wave-domain algorithm for scenarios with a moving primary noise source to further emphasize its advantage over the closed-loop LMS algorithm.

Environmental sound identification and recognition aim to detect sound events within an audio clip. This technology is useful in many real-world applications such as security systems, smart vehicle navigation and surveillance of noise pollution, etc. Research on this topic has received increased attention in recent years. Performance is increasing rapidly as a result of deep learning methods. In this project, our goal is to realize urban sound classification using several neural network models. We select log-Mel spectrogram as the audio representation and use two types of neural networks to perform the classification task. The first is the convolutional neural network (CNN), which is the most straightforward and widely used method for a classification problem. The second type of network is autoencoder based models. This type of model includes the variational autoencoder (VAE), beta-VAE and bounded information rate variational autoencoder (BIR-VAE). The encoders of these systems extract a low dimensionality representation. The classification is then performed on this so-called latent representation. Our experiments assess the performances of different models by evaluation metrics. The results show that CNN is the most promising classifier in our case, autoencoder-based models can successfully reconstruct the log-Mel spectrogram and the latent features learned by encoders are meaningful as classification can be achieved.

Listening in noise is a challenging problem that affects the hearing capability of not only normal hearing but especially hearing impaired people. Since the last four decades, enhancing the quality and intelligibility of noise corrupted speech by reducing the effect of noise has been addressed using statistical signal processing techniques as well as neural networks. However, the fundamental idea behind implementing these methods is the same, i.e., to achieve the best possible estimate of a single target speech waveform. This thesis explores a different route using generative modeling with deep neural networks where speech is artificially generated by conditioning the model on previously predicted samples and features extracted from noisy speech. The proposed system consists of the U-Net model for enhancing the noisy features and the WaveRNN synthesizer (originally proposed for text-to-speech synthesis) re-designed for synthesizing clean sounding speech from noisy features. Subjective results indicate that speech generated by the proposed system is preferred over listening to noisy speech however, the improvement in intelligibility is not significant.

Following their conception in the mid twentieth century, the world of computers has evolved from a landscape of isolated entities into a sprawling web of interconnected machines. Yet, given this evolution, many of the methods we use for allowing computers to work together still reflect their inherently isolated origins with the aggregation of data or master-slave relationships still commonly seeing use. While sufficient for some types of applications, these approaches do not naturally reflect the collaboration strategies we observe in nature and so the question is raised as to whether we can do better?

In parallel to the improvements in computer to computer communication, the emergence of new paradigms such as the Internet of Things (IoT), Big Data processing and cloud computing in recent years has placed an increasing importance on networked systems in many facets of the modern world. From power grid management, to autonomous vehicle navigation, to even our basic means of interaction through social media, these networks are a pervasive presence in our day to day lives. The vast amounts of data generated by these networks and their ever increasing sizes makes it impractical if not impossible to resort to traditional centralized processing and therefore necessitates the search for new methods of signal processing within networked systems.

In this thesis we approach the task of distributed signal processing by exploiting the synergy between such tasks and equivalent convex optimization problems. Specifically, we focus on the task of distributed convex optimization, that of solving optimization problems involving groups of computers in a collaborative manner and the development of distributed solvers for such tasks. Such solvers distinguish themselves by only allowing local computations at each computer in a network and the exchange of information between connected computers. In this way, distributed solvers naturally respect the structure of the underlying network in which they are deployed.

In the pursuit of our goal, we approach the task of distributed solver design via the lens of monotone operator theory. Providing a well known platform for the derivation of many first order convex solvers, herein we demonstrate the use of this theory as a means of constructing and analyzing a number of algorithms for distributed optimization. The first major contribution of this thesis lies in the analysis and understanding of an existing algorithm for distributed optimization within the literature termed the primal dual method of multipliers (PDMM). In particular, by demonstrating a novel interpretation of PDMM from the perspective of monotone operator theory we are able to better understand its convergent characteristics and highlight sufficient conditions for which PDMM will converge at a geometric rate. Furthermore we quantify the impact that network topology has on these convergence rates, drawing a direct connection between spectral characteristics of networks and distributed optimization.

Secondly, we explored the space of solver design by proposing novel algorithms for distributed networks. For the family of separable optimization problems, those with separable objectives and constraints, we demonstrated a distributed solver design using a specific lifted dual form. Based on monotone operator theory, the convergence analysis of the proposed method followed naturally from well known results and broadened the class of distributable problems compared to the likes of PDMM. Furthermore, in the case of time-varying consensus problems, we again proposed a new algorithm by combining a network dependent metric choice with classic operator splitting methods. Again the monotone basis of this algorithm facilitated the convergence analysis of this method which empirically was also shown to converge for general closed, convex and proper functions.

Finally, we demonstrated how these methods could be used for practical distributed signal processing in networks by considering the case of multichannel speech enhancement in wireless acoustic sensor networks. By combining a particular modeling of the acoustic scene with the algorithms mentioned above, the proposed method was not only distributable but also offered increased resilience to steering vector mismatch than other standard approaches. This example also highlights the importance of understanding both the target application and the distributed solvers themselves in developing effective solutions.

Overall, this thesis provides a first foray into the world of distributed optimization via the lens of monotone operator theory. We feel that this perspective provides an ideal reference for the analysis of such algorithms while also providing a general framework for convex optimization solver design in turn. While this thesis is not the end of this branch of research, it indicates the potential of the monotone operator theory as a unifying method for the development and analysis of distributed optimization solutions.