Stephan Weiss

• PhD, Dipl.-Ing.
• Lecturer at University of Strathclyde

A matrix of analytic functions A(z), such as the matrix of transfer functions in a multiple-input multiple-output (MIMO) system, generally admits an analytic singular value decomposition (SVD), where the singular values themselves are functions. When evaluated on the unit circle, for the sake of analyticity, these singular values must be permitted...

This paper investigates the performance of a likelihood ratio test in combination with a polynomial subspace projection approach to detect weak transient signals in broadband array data. Based on previous empirical evidence that a likelihood ratio test is advantageously applied in a lower-dimensional subspace, we present analysis that highlights ho...

We investigate the singular value decomposition (SVD) of a rectangular matrix A ( z ) of functions that are analytic on an annulus that includes at least the unit circle. Such matrices occur, e.g., as matrices of transfer functions representing broadband multiple-input multiple-output systems. Our analysis is based on findings for the analytic S...

Broadband sensor array problems can be formulated using parahermitian polynomial matrices, and the optimal solution to these problems can be based on the eigenvalue decomposition (EVD) of these matrices. An algorithm has been proposed in the past to extract analytic eigenvalues of parahermitian matrices, but it does not scale well with the temporal...

This article is devoted to the polynomial eigenvalue decomposition (PEVD) and its applications in broadband multichannel signal processing, motivated by the optimum solutions provided by the EVD for the narrowband case [1] , [2] . In general, we would like to extend the utility of the EVD to also address broadband problems. Multichannel broadba...

In the narrowband case, the best least squares approximation of a matrix by a unitary one is given by the Procrustes problem. In this paper, we expand this idea to matrices of analytic functions, and characterise a broadband equivalent to the narrowband case: the polynomial Procrustes problem. Its solution is based on an analytic singular value dec...

An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors. We have previously defined a discrete Fourier transform (DFT) domain algorithm which has been proven to extract the analytic eigenvalues. The selection of the eigenvalues as analytic functions guarantees in turn...

Multi-channel signals captured by spatially separated sensors often contain a high level of data redundancy. A compact signal representation enables more efficient storage and processing, which has been exploited for data compression, noise reduction, and speech and image coding. This paper focuses on the compact representation of speech signals ac...

Voice activity detection (VAD) algorithms are essential for many speech processing applications, such as speaker diarization, automatic speech recognition, speech enhancement, and speech coding. With a good VAD algorithm, non-speech segments can be excluded to improve the performance and computation of these applications. In this paper, we propose...

A voice activity detection (VAD) algorithm identifies whether or not time frames contain speech. It is essential for many military and commercial speech processing applications, including speech enhancement, speech coding, speaker identification, and automatic speech recognition. In this work, we adopt earlier work on detecting weak transient signa...

Direction of arrival (DoA) estimation for sound source localization is increasingly prevalent in modern devices. In this paper, we explore a polynomial extension to the multiple signal classification (MUSIC) algorithm, spatio-spectral polynomial (SSP)-MUSIC, and evaluate its performance when using speech sound sources. In addition, we also propose...

An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with analytic eigenvalues and eigen\-vectors except in the case of multiplexed data. In this paper, we propose an iterative algorithm for the estimation of the analytic eigenvalues. Since these are generally transcendental, we find a polynomial approximation with a defined er...

A number of algorithms are capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD), which is a generalisation of the EVD and will diagonalise a parahermitian polynomial matrix via paraunitary operations. While offering promising results in various broadband array processing applications, the PEVD has seen limited depl...

Health state assessment of wind turbine components has become a vital aspect of wind farm operations in order to reduce maintenance costs. The gearbox is one of the most costly components to replace and it is usually monitored through vibration condition monitoring. This study aims to present a review of the most popular existing gear vibration dia...

The ensemble-optimum support for a sample space-time covariance matrix can be determined from the ground truth space-time covariance, and the variance of the estimator. In this paper we provide approximations that permit the estimation of the sample-optimum support from the estimate itself, given a suitable detection threshold. In simulations, we p...

Presents corrections to the paper, “On the existence and uniqueness of the eigenvalue decomposition of a paraher mitian matrix,” (Weiss, S. et al), IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2659–2672, May 2018.

This research investigates the prediction of failure and remaining useful life (RUL) of gearboxes for modern multi‐megawatt wind turbines. Failure and RUL are predicted through the use of machine learning techniques and large amounts of labelled wind turbine supervisory control and data acquisition (SCADA) and vibration data. The novelty of this wo...

This paper presents a methodology for predicting planet bearing failures utilising vibration data acquired through accelerometers installed on the gearbox surface. The proposed methodology applies certain signal pre-processing techniques in order to remove the speed variations of the turbine and separate the stochastic bearing components from the d...

This paper studies the impact of estimation errors in the sample space-time covariance matrix on its parahermitian matrix eigenvalue decomposition. We provide theoretical bounds for the perturbation of the ground-truth eigenvalues and of the subspaces of their corresponding eigenvectors. We show that for the eigenvalues, the perturbation depends on...

This paper addresses the extension of the factorisation of a Hermitian matrix by an eigenvalue decomposition (EVD) to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle. Such parahermitian matrices contain polynomials or rational functions in the complex variable z, and arise e.g. as cross spectral...

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polyno...

Studies have shown that a large geographic spread of installed capacity can reduce wind power variability and smooth production. This could be achieved by using electricity interconnections and storage systems. However, interconnections and storage are not totally flexible, so it is essential to understand the wind power correlation in order to add...

Uniform placement of array elements limits its maximum frequency due to the formation of grating lobes. While non-uniform element or subarray spacing have significantly lower grating lobes, it reduces aperture efficiency and leads to arrays that are difficult to design and manufacture. We propose a modular asymmetric convex-shaped subarray to const...

In recent years, several algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cy...

A number of algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. This paper addresses savings — both computationally and in terms of memory use — that exploit the p...

In this work we present a new method of controlling the order growth of polynomial matrices in the multiple shift second order sequential best rotation (MS-SBR2) algorithm which has been recently proposed by the authors for calculating the polynomial matrix eigenvalue decomposition (PEVD) for para-Hermitian matrices. In effect, the proposed method...

This chapter discusses the single carrier modulation techniques which have been proposed and used in first generation narrowband PLC systems. It emphasizes the recent insight and research focusing first on frequency/phase shift keying combined with permutation coding. The chapter covers multicarrier modulation which is at the heart of latest narrow...

In this paper, we consider minimum-mean-square error (MMSE) training-based channel estimation for two-hop multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) relaying systems. The channel estimation process is divided into two main phases. The relay-destination channel is estimated in the first phase and can be o...

Recently a selection of sequential matrix diagonalisation (SMD) algorithms have been introduced which approximate polynomial eigenvalue decomposition of parahermitian matrices. These variants differ only in the search methods that are used to bring energy onto the zero-lag. Here we analyse the search methods in terms of their computational complexi...

In this paper, we present a new multichannel spectral factorization algorithm which can be utilized to calculate the approximate spectral factor of any para-Hermitian polynomial matrix. The proposed algorithm is based on an iterative method for polynomial matrix eigenvalue decomposition (PEVD). By using the PEVD algorithm, the multichannel spectral...

In this paper, we present an improved version of the second order sequential best rotation algorithm (SBR2) for polynomial matrix eigenvalue decomposition of para-Hermitian matrices. The improved algorithm is entitled multiple shift SBR2 (MS-SBR2) which is developed based on the original SBR2 algorithm. It can achieve faster convergence than the or...

This paper presents initial progress on formulating minimum variance distortionless response (MVDR) broadband beamforming using a generalised sidelobe canceller (GSC) in the context of polynomial matrix techniques. The quiescent vector is defined as a broadband steering vector, and we propose a blocking matrix design obtained by paraunitary matrix...

In this paper, we show that the paraunitary (PU) matrices that arise from the polynomial eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique. In particular, arbitrary shifts (delays) of polynomials in one row of a PU matrix yield another PU matrix that admits the same PEVD. To keep the order of such a PU matrix as low as possib...

Communication over doubly selective channels (both time and frequency selective) suffers from significant intercarrier interference (ICI). This problem is severe in underwater acoustic communications. In this paper, a new Partial Fractional Fourier (PFrFT) based orthogonal frequency division multiplex (OFDM) scenario is presented for dealing with s...

Two nonlinear methods for producing short-term spatio-temporal wind speed forecast are presented. From the relatively new class of kernel methods, a kernel least mean squares algorithm and kernel recursive least squares algorithm are introduced and used to produce 1 to 6 hour-ahead predictions of wind speed at six locations in the Netherlands. The...

For transceivers operating in television white space (TVWS), frequency agility and strict spectral mask fulfilments are vital. In the UK, TVWS covers a 320 MHz wide frequency band in the UHF range, and the aim of this paper is to present a wideband digital up- and down converter for this scenario. Sampling at RF, a two stage digital conversion is p...

This paper explores how the accuracy of short-term prediction of wind speed and direction can be enhanced by considering the diurnal variation of the wind. The wind speed and direction are modelled as the magnitude and phase of a complex-valued time series. The prediction is performed by a multichannel filter using the spatio-temporal correlation b...

Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matri...

Polynomial parahermitian matrices can accurately and elegantly capture the space-time covariance in broadband array problems. To factorise such matrices, a number of polynomial EVD (PEVD) algorithms have been suggested. At every step, these algorithms move various amounts of off-diagonal energy onto the diagonal, to eventually reach an approximate...

The Multiple Shift Maximum Element Sequential Matrix Diagonalisation (MSME-SMD) algorithm is a powerful but costly method for performing approximate polynomial eigenvalue decomposition (PEVD) for space-time covariance-type matrices encountered in e.g. broadband array processing. This paper discusses a newly developed search method that restricts th...

Future television white space (TVWS) transceivers require frequency agility and adherence to spectral masks. For the 320 MHz wide UHF range for TVWS in the UK, this paper discusses two variations of a design for wideband digital up- and down converters at are capable of sampling at radio frequency. The designs consist of a two stage digital convers...

The short term forecasting of wind speed and direction has previously been improved by adopting a cyclo-stationary multichannel linear prediction approach which incorporated seasonal cycles into the estimation of statistics. This paper expands previous analysis by also incorporating diurnal variation and time-dependent window lengths. Based on a la...

This paper expands on a recent polynomial matrix formulation for a minimum variance distortionless response (MVDR) broadband beamformer. Within the polynomial matrix framework, this beamformer is a straightforward extension from the narrowband case, and offers advantages in terms of complexity and robustness particularly for off-broadside constrain...