Portable High-definition Audio Spectrum Analyzer

The Portable High-definition Audio Spectrum Analyzer (PHASA) allows the user to visualize the audio frequency spectrum of an incoming line-level stereo audio signal. Upon pressing the touch screen spectrum graph, the PHASA displays the corresponding frequency and volume levels as well as crosshairs at the touched location. The PHASA features multiple left/right channel display modes— Left channel only, right channel only, both channels simultaneously, and the average between the two channels. The PHASA features multiple resolution display modes (standard-resolution and high-resolution) and multiple dynamics display modes (standard dynamics, averaging, and peak/hold). The PHASA accepts input audio via a 1/4 TRS jack and outputs via a 1/4 TRS jack. When activated, the output jack outputs a stereo white noise signal for measuring the frequency response of external equipment. This capability makes the PHASA a useful tool for frequency response characterization of audio equipment, which allows for more informed audio engineering design decisions

Distributed processing of a fractal array beamformer

Fractals have been proven as potential candidates for satellite flying formations, where its different elements represent a thinned array. The distributed and low power nature of the nodes in this network motivates distributed processing when using such an array as a beamformer. This paper proposes such initial idea, and demonstrates that benefits such as strictly limited local processing capability independent of the array’s dimension and local calibration can be bought at the expense of a slightly increased overall cost

Multiple shift second order sequential best rotation algorithm for polynomial matrix EVD

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 algorithmis entitledmultiple shift SBR2 (MS-SBR2) which is developed based on the original SBR2 algorithm. It can achieve faster convergence than the original SBR2 algorithm by means of transferring more off-diagonal energy onto the diagonal at each iteration. Its convergence is proved and also demonstrated by means of a numerical example. Furthermore, simulation results are included to compare its convergence characteristics and computational complexity with the original SBR2, sequential matrix diagonalization (SMD) and multiple shift maximum element SMD algorithms

Order-controlled multiple shift SBR2 algorithm for para-hermitian polynomial matrices

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 introduces a new elementary delay strategy which keeps all the row (column) shifts in the same direction throughout each iteration, which therefore gives us the flexibility to control the polynomial order growth by selecting shifts that ensure non-zero coefficients are kept closer to the zero-lag plane. Simulation results confirm that further order reductions of polynomial matrices can be achieved by using this direction-fixed delay strategy for the MS-SBR2 algorithm

Investigation of a polynomial matrix generalised EVD for multi-channel Wiener filtering

State of the art narrowband noise cancellation techniques utilise the generalised eigenvalue decomposition (GEVD) for multichannel Wiener filtering which can be applied to independent frequency bins in order to achieve broadband processing. Here we investigate the extension of the GEVD to broadband, polynomial matrices, akin to strategies that have already been developed by McWhirter et. al on the polynomial matrix eigenvalue decomposition (PEVD)

Polynomial subspace decomposition for broadband angle of arrival estimation

In this paper we study the impact of polynomial or broadband subspace decompositions on any subsequent processing, which here uses the example of a broadband angle of arrival estimation technique using a recently proposed polynomial MUSIC (P-MUSIC) algorithm. The subspace decompositions are performed by iterative polynomial EVDs, which differ in their approximations to diagonalise and spectrally majorise s apce-time covariance matrix.We here show that a better diagonalisation has a significant impact on the accuracy of defining broadband signal and noise subspaces, demonstrated by a much higher accuracy of the P-MUSIC spectrum

Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

A number of algorithms capable of iteratively calculating 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. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays

Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

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 possible, we pro- pose a row-shift correction. Using the example of an iterative PEVD algorithm with previously proposed truncation of the PU matrix, we demonstrate that a considerable shortening of the PU order can be accomplished when using row-corrected truncation

Shortening of paraunitary matrices obtained by polynomial eigenvalue decomposition algorithms

This paper extends the analysis of the recently introduced row-shift corrected truncation method for paraunitary matrices to those produced by the state-of-the-art sequential matrix diagonalisation (SMD) family of polynomial eigenvalue decomposition (PEVD) algorithms. The row-shift corrected truncation method utilises the ambiguity in the paraunitary matrices to reduce their order. The results presented in this paper compare the effect a simple change in PEVD method can have on the performance of the paraunitary truncation. In the case of the SMD algorithm the benefits of the new approach are reduced compared to what has been seen before however there is still a reduction in both reconstruction error and paraunitary matrix order

Maximum energy sequential matrix diagonalisation for parahermitian matrices

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 matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step