Analytic expressions are derived for the eigenfunctions and eigenvalues of Laplace transform similar dilationally invariant integral equations first kind. Some generalised concepts information theory introduced to show how use these enables maximum possible amount be obtained when solving inverse problem numerically. These also explain available depends on level noise in calculation structure particular kernel. numerical examples which illustrate points presented.

We investigate the singular value decomposition (SVD) of a rectangular matrix <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ( xmlns:xlink="http://www.w3.org/1999/xlink">z</i> ) functions that are analytic on an annulus includes at least unit circle. Such matrices occur, e.g., as transfer representing broadband multiple-input multiple-output systems. Our analysis is based findings for SVD applicable to continuous time systems, and...

A systolic array for performing recursive least-squares minimization is desc/ performs an orthogonal triangularization of the data matrix using a pipelined SE© (1983) COPYRIGHT SPIE--The International Society Optical Engineering. Downloading abstract permitted personal use only.

For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) generalized a matrix EVD (PEVD). In this paper, new iterative PEVD algorithm based on sequential diagonalization (SMD) is introduced. At every step SMD shifts dominant column or row of zero lag position and eliminates resulting instantaneous correlation. A proof convergence provided, it demonstrated that...

A novel algorithm and architecture are described which have specific application to high performance, digital, adaptive beamforming. It is shown how a simple, linearly constrained combiner forms the basis for wide range of antenna subsystems. The function such an formulated as recursive least squares minimization operation corresponding weight vector obtained by means <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q-R</tex> decomposition using...

The problem of paraunitary filter bank design for subband coding has received considerable attention in recent years, not least because the energy preserving property this class banks.In paper, we consider signal-adapted, finite impulse response (FIR), banks using polynomial matrix EVD (PEVD) techniques.Modifications are proposed to an iterative, time-domain PEVD method, known as sequential best rotation (SBR2) algorithm, which enables its effective application FIR orthonormal efficient...

This article is devoted to the polynomial eigenvalue decomposition (PEVD) and its applications in broadband multichannel signal processing, motivated by optimum solutions provided EVD for narrowband case <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , rid="ref2" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> . In general, we would like extend utility of also address problems. Multichannel signals...

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to matrices. purpose this article provide a review theoretical foundations PEVD and highlight practical applications in area broadband blind source separation (BSS). Based on basic definitions terminology such as parahermitian paraunitary matrices, strong decorrelation spectral majorisation, its will be briefly outlined. paper then focuses applicability subspace techniques — enabled by...

In this paper, a new algorithm for calculating the QR decomposition (QRD) of polynomial matrix is introduced. This amounts to transforming upper triangular form by application series paraunitary matrices such as elementary delay and rotation matrices. It shown that can also be used formulate singular value (SVD) matrix, which essentially diagonalizing again Example are demonstrate both types decomposition. Mathematical proofs convergence decompositions outlined. Finally, possible in...

A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing approaches, eliminates more off-diagonal energy per step. This leads faster convergence while incurring only a marginal increase in complexity. We motivate approach, prove its convergence, and demonstrate some results that...

The least squares lattice algorithm for adaptive filtering based on the technique of QR decomposition (QRD) is derived from first principles. In common with other algorithms filtering, this only requires O(p) operations solution a pth order problem. has as its root QRDbased recursive minimisation and hence expected to have superior numerical properties when compared fast algorithms. This contains within it QRD-based solving linear prediction presented in two forms: one that involves taking...

The use of systolic arrays 1-bit cells to implement a range important signal processing functions is demonstrated. Two examples, pipelined multiplier and bit-slice transform circuit, are given. This approach has many implications for silicon technology, these outlined briefly.

In this paper, we show that the paraunitary (PU) matrices arise from polynomial eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique. particular, arbitrary shifts (delays) polynomials in one row PU yield another admits same PEVD. To keep order such as low possible, propose row-shift correction. Using example an iterative PEVD algorithm with previously proposed truncation matrix, demonstrate considerable shortening can be accomplished when using row-corrected truncation.

In this paper, we present an improved version of the second order sequential best rotation algorithm (SBR2) for polynomial matrix eigenvalue decomposition para-Hermitian matrices. The is entitled multiple shift SBR2 (MS-SBR2) which developed based on original algorithm. It can achieve faster convergence than by means transferring more off-diagonal energy onto diagonal at each iteration. Its proved and also demonstrated a numerical example. Furthermore, simulation results are included to...

Abstract Effective models for fitting a whole range of photon-correlation data are described. They incorporate the maximum number degrees freedom which may be used without fit becoming unstable due to ill-conditioning and lead computer program is extremely fast readily implemented on minicomputer. The results some preliminary calculations laser anemometry macromolecular polydispersity presented.

A large family of broadband angle arrival estimation algorithms are based on the coherent signal subspace (CSS) method, whereby focussing matrices appropriately align covariance across narrowband frequency bins. In this paper, we analyse an auto-focussing approach in framework polynomial matrix decompositions, leading to comparisons two recently proposed multiple classification (MUSIC) algorithms. The analysis is complemented with numerical simulations.

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of errors. In this paper, we propose an OSFB-based coder a correlated additive Gaussian noise channel, which covariance matrix is assumed known. Based on suitable factorisation matrix, develop design decoder's synthesis bank in order minimise power decoded signal, subject admitting perfect reconstruction through paraunitarity bank. We...

We show how the architecture of two recently reported bit-level systolic array circuits—a single-bit coefficient correlator and a multibit convolver—may be modified to incorporate unidirectional data flow. This feature has some important advantages in terms chip cascadability, fault tolerance possible wafer-scale integration.