Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\chi$ is a $k$-valued character for $G$ with $\chi(a)\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over $H'$ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over $H$ and $H'$, and classify them. Finally, when $\chi(a)$ is a primitive $n$-th root of unity for some $n>2$, we determine all finite dimensional indecomposable projective objects in the category of weight modules over $H'$.Comment: arXiv admin note: substantial text overlap with arXiv:1206.394

Beamforming and Direction of Arrival Estimation Based on Vector Sensor Arrays

Array signal processing is a technique linked closely to radar and sonar systems. In communication, the antenna array in these systems is applied to cancel the interference, suppress the background noise and track the target sources based on signals'parameters. Most of existing work ignores the polarisation status of the impinging signals and is mainly focused on their direction parameters. To have a better performance in array processing, polarized signals can be considered in array signal processing and their property can be exploited by employing various electromagnetic vector sensor arrays. In this thesis, firstly, a full quaternion-valued model for polarized array processing is proposed based on the Capon beamformer. This new beamformer uses crossed-dipole array and considers the desired signal as quaternion-valued. Two scenarios are dealt with, where the beamformer works at a normal environment without data model errors or with model errors under the worst-case constraint. After that, an algorithm to solve the joint DOA and polarisation estimation problem is proposed. The algorithm applies the rank reduction method to use two 2-D searches instead of a 4-D search to estimate the joint parameters. Moreover, an analysis is given to introduce the difference using crossed-dipole sensor array and tripole sensor array, which indicates that linear crossed-dipole sensor array has an ambiguity problem in the estimation work and the linear tripole sensor array avoid this problem effectively. At last, we study the problem of DOA estimation for a mixture of single signal transmission (SST) signals and duel signal transmission (DST) signals. Two solutions are proposed: the first is a two-step method to estimate the parameters of SST and DST signals separately; the second one is a unified one-step method to estimate SST and DST signals together, without treating them separately in the estimation process

Noise Types Adaptation for Speech Enhancement with Recurrent Neural Network

Speech enhancement is a critical part in automatic speech recognition systems. Recently with the development of deep learning based techniques, those speech enhancement systems trained with neural networks can significantly improve performance. While many of the latest speech enhancement systems show advantages in maximizing the perceptual quality of the noisy signals, they expose drawbacks when the test noisy signals have noise types that never exist during the system training process. The systems have relatively poor performance when handling noisy signals with unseen noise in contrast to noisy signals with seen noise. The dissimilarity between the training and testing circumstances can cause a serious performance decline in a deep learning task.In this work, a new method is proposed to solve the noise types problem. The framework has three parts: the autoencoder, the gradient reverse layers and the recurrent neural networks. The proposed framework can weaken the noise types influences when handling random noisy signals. This work shows that the new method outperforms the baseline models in unseen noise situations