The Nehari Shuffle: FIR(q) Filter Design With Guaranteed Error Bounds

This paper presents a new approach to the problem of designing a finite impulse response filter of specified length, q, which approximates in uniform frequency (L-infinity) norm a given desired (possibly infinite impulse responmse) causal, stable filter transfer function. We derive an algorithm-independent lower bound on the achievable approximation error and then present and approximation method which involves the solution of a fixed number of all-pass (Nehari) extension problems and so is called the Nehari shuffle. Upper and lower bounds on the approximation error are derived for the algorithm. These bounds are calculable a priori so the length of the filter can be found before designing the filter. Examples indicate that the method closely approaches the derived global lower bound. We compare the new method with the Preuss (complex Remez exchange) algorithm in some examples

FIR(q) Filter Design Without the Linear Phase Contraint

This paper presents a new approach to the problem of designing a finite impulse response filter of specified length, q, which approximates in uniform frequency norm a given desired (possibly infinite impulse response) filter transfer function

Data compression for estimation of the physical parameters of stable and unstable linear systems

A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a nonlinear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework as stable systems. Experimental data are used to demonstrate the efficacy of the proposed approach

Reducing broad-spectrum antibiotic use in intensive care unit between first and second waves of COVID-19 did not adversely affect mortality

Background: The COVID-19 pandemic increased the use of broad-spectrum antibiotics due to diagnostic uncertainty, particularly in critical care. Multi-professional communication became more difficult, weakening stewardship activities. Aim: To determine changes in bacterial co-/secondary infections and antibiotics used in COVID-19 patients in critical care, and mortality rates, between the first and second waves. Methods: Prospective audit comparing bacterial co-/secondary infections and their treatment during the first two waves of the pandemic in a single-centre teaching hospital intensive care unit. Data on demographics, daily antibiotic use, clinical outcomes, and culture results in patients diagnosed with COVID-19 infection were collected over 11 months. Findings: From March 9th, 2020 to September 2nd, 2020 (Wave 1), there were 156 patients and between September 3rd, 2020 and February 1st, 2021 (Wave 2) there were 235 patients with COVID-19 infection admitted to intensive care. No significant difference was seen in mortality or positive blood culture rates between the two waves. The proportion of patients receiving antimicrobial therapy (93.0% vs 81.7%; P < 0.01) and the duration of meropenem use (median (interquartile range): 5 (2–7) vs 3 (2–5) days; P = 0.01) was lower in Wave 2. However, the number of patients with respiratory isolates of Pseudomonas aeruginosa (4/156 vs 21/235; P < 0.01) and bacteraemia from a respiratory source (3/156 vs 20/235; P < 0.01) increased in Wave 2, associated with an outbreak of infection. There was no significant difference between waves with respect to isolation of other pathogens. Conclusion: Reduced broad-spectrum antimicrobial use in the second wave of COVID-19 compared with the first wave was not associated with significant change in mortality

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

A web site navigation engine

Often users navigating (or “surfing”) through a web site “get lost in hyperspace”, when they lose the context in which they are browsing, and are unsure how to proceed in terms of satisfying their original goal. The unresolved problem in web site usability, of assisting users in finding their way, is termed the navigation problem. (See [LL00] for a survey and critique on the navigation problem.) This problem is becoming even more acute with the continuing growth of web sites in terms of their structure, which is becoming more complex, and the vast amount information they intend to deliver. In contrast users are not willing to invest time to learn this structure and expect the delivery of the relevant content without delay. To tackle this problem we are developing a navigation system for semi-automating user navigation which builds trails of information, i.e. sequences of linked pages, which are relevant to the user query. The preferred trails are presented to the user in a tree-like structure which they can interact with. This is in sharp contrast to a search engine which merely outputs a list of pages which are relevant to the user query without addressing the problem of which trail the user should follow. We discuss the architecture of the navigation system and give a brief description of the navigation engine and user interface