A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

A 64-point Fourier transform chip for high-speed wireless LAN application using OFDM

In this article, we present a novel fixed-point 16-bit word-width 64-point FFT/IFFT processor developed primarily for the application in the OFDM based IEEE 802.11a Wireless LAN (WLAN) baseband processor. The 64-point FFT is realized by decomposing it into a 2-D structure of 8-point FFTs. This approach reduces the number of required complex multiplications compared to the conventional radix-2 64-point FFT algorithm. The complex multiplication operations are realized using shift-and-add operations. Thus, the processor does not use any 2-input digital multiplier. It also does not need any RAM or ROM for internal storage of coefficients. The proposed 64-point FFT/IFFT processor has been fabricated and tested successfully using our in-house 0.25 ?m BiCMOS technology. The core area of this chip is 6.8 mm2. The average dynamic power consumption is 41 mW @ 20 MHz operating frequency and 1.8 V supply voltage. The processor completes one parallel-to-parallel (i. e., when all input data are available in parallel and all output data are generated in parallel) 64-point FFT computation in 23 cycles. These features show that though it has been developed primarily for application in the IEEE 802.11a standard, it can be used for any application that requires fast operation as well as low power consumption

Number theoretic techniques applied to algorithms and architectures for digital signal processing

Many of the techniques for the computation of a two-dimensional convolution of a small fixed window with a picture are reviewed. It is demonstrated that Winograd's cyclic convolution and Fourier Transform Algorithms, together with Nussbaumer's two-dimensional cyclic convolution algorithms, have a common general form. Many of these algorithms use the theoretical minimum number of general multiplications. A novel implementation of these algorithms is proposed which is based upon one-bit systolic arrays. These systolic arrays are networks of identical cells with each cell sharing a common control and timing function. Each cell is only connected to its nearest neighbours. These are all attractive features for implementation using Very Large Scale Integration (VLSI). The throughput rate is only limited by the time to perform a one-bit full addition. In order to assess the usefulness to these systolic arrays a 'cost function' is developed to compare them with more conventional techniques, such as the Cooley-Tukey radix-2 Fast Fourier Transform (FFT). The cost function shows that these systolic arrays offer a good way of implementing the Discrete Fourier Transform for transforms up to about 30 points in length. The cost function is a general tool and allows comparisons to be made between different implementations of the same algorithm and between dissimilar algorithms. Finally a technique is developed for the derivation of Discrete Cosine Transform (DCT) algorithms from the Winograd Fourier Transform Algorithm. These DCT algorithms may be implemented by modified versions of the systolic arrays proposed earlier, but requiring half the number of cells

Stochastic arrays and learning networks

This thesis presents a study of stochastic arrays and learning networks. These arrays will be shown to consist of simple elements utilising probabilistic coding techniques which may interact with a random and noisy environment to produce useful results. Such networks have generated considerable interest since it is possible to design large parallel self-organising arrays of these elements which are trained by example rather than explicit instruction. Once the learning process has been completed, they then have the potential ability to form generalisations, perform global optimisation of traditionally difficult problems such as routing and incorporate an associative memory capability which can enable such tasks as image recognition and reconstruction to be performed, even when given a partial or noisy view of the target. Since the method of operation of such elements is thought to emulate the basic properties of the neurons of the brain, these arrays have been termed neural 'networks. The research demonstrates the use of stochastic elements for digital signal processing by presenting a novel systolic array, utilising a simple, replicated cell structure, which is shown to perform the operations of Cyclic Correlation and the Discrete Fourier Transform on inherently random and noisy probabilistic single bit inputs. This work is then extended into the field of stochastic learning automata and to neural networks by examining the Associative Reward-Punish (A(_R-P)) pattern recognising learning automaton. The thesis concludes that all the networks described may potentially be generalised to simple variations of one standard probabilistic element utilising stochastic coding, whose properties resemble those of biological neurons. A novel study is presented which describes how a powerful deterministic algorithm, previously considered to be biologically unviable due to its nature, may be represented in this way. It is expected that combinations of these methods may lead to a series of useful hybrid techniques for training networks. The nature of the element generalisation is particularly important as it reveals the potential for encoding successful algorithms in cheap, simple hardware with single bit interconnections. No claim is made that the particular algorithms described are those actually utilised by the brain, only to demonstrate that those properties observed of biological neurons are capable of endowing collective computational ability and that actual biological algorithms may perhaps then become apparent when viewed in this light

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Automatic analysis and classification of cardiac acoustic signals for long term monitoring

Objective: Cardiovascular diseases are the leading cause of death worldwide resulting in over 17.9 million deaths each year. Most of these diseases are preventable and treatable, but their progression and outcomes are significantly more positive with early-stage diagnosis and proper disease management. Among the approaches available to assist with the task of early-stage diagnosis and management of cardiac conditions, automatic analysis of auscultatory recordings is one of the most promising ones, since it could be particularly suitable for ambulatory/wearable monitoring. Thus, proper investigation of abnormalities present in cardiac acoustic signals can provide vital clinical information to assist long term monitoring. Cardiac acoustic signals, however, are very susceptible to noise and artifacts, and their characteristics vary largely with the recording conditions which makes the analysis challenging. Additionally, there are challenges in the steps used for automatic analysis and classification of cardiac acoustic signals. Broadly, these steps are the segmentation, feature extraction and subsequent classification of recorded signals using selected features. This thesis presents approaches using novel features with the aim to assist the automatic early-stage detection of cardiovascular diseases with improved performance, using cardiac acoustic signals collected in real-world conditions. Methods: Cardiac auscultatory recordings were studied to identify potential features to help in the classification of recordings from subjects with and without cardiac diseases. The diseases considered in this study for the identification of the symptoms and characteristics are the valvular heart diseases due to stenosis and regurgitation, atrial fibrillation, and splitting of fundamental heart sounds leading to additional lub/dub sounds in the systole or diastole interval of a cardiac cycle. The localisation of cardiac sounds of interest was performed using an adaptive wavelet-based filtering in combination with the Shannon energy envelope and prior information of fundamental heart sounds. This is a prerequisite step for the feature extraction and subsequent classification of recordings, leading to a more precise diagnosis. Localised segments of S1 and S2 sounds, and artifacts, were used to extract a set of perceptual and statistical features using wavelet transform, homomorphic filtering, Hilbert transform and mel-scale filtering, which were then fed to train an ensemble classifier to interpret S1 and S2 sounds. Once sound peaks of interest were identified, features extracted from these peaks, together with the features used for the identification of S1 and S2 sounds, were used to develop an algorithm to classify recorded signals. Overall, 99 features were extracted and statistically analysed using neighborhood component analysis (NCA) to identify the features which showed the greatest ability in classifying recordings. Selected features were then fed to train an ensemble classifier to classify abnormal recordings, and hyperparameters were optimized to evaluate the performance of the trained classifier. Thus, a machine learning-based approach for the automatic identification and classification of S1 and S2, and normal and abnormal recordings, in real-world noisy recordings using a novel feature set is presented. The validity of the proposed algorithm was tested using acoustic signals recorded in real-world, non-controlled environments at four auscultation sites (aortic valve, tricuspid valve, mitral valve, and pulmonary valve), from the subjects with and without cardiac diseases; together with recordings from the three large public databases. The performance metrics of the methodology in relation to classification accuracy (CA), sensitivity (SE), precision (P+), and F1 score, were evaluated. Results: This thesis proposes four different algorithms to automatically classify fundamental heart sounds – S1 and S2; normal fundamental sounds and abnormal additional lub/dub sounds recordings; normal and abnormal recordings; and recordings with heart valve disorders, namely the mitral stenosis (MS), mitral regurgitation (MR), mitral valve prolapse (MVP), aortic stenosis (AS) and murmurs, using cardiac acoustic signals. The results obtained from these algorithms were as follows: • The algorithm to classify S1 and S2 sounds achieved an average SE of 91.59% and 89.78%, and F1 score of 90.65% and 89.42%, in classifying S1 and S2, respectively. 87 features were extracted and statistically studied to identify the top 14 features which showed the best capabilities in classifying S1 and S2, and artifacts. The analysis showed that the most relevant features were those extracted using Maximum Overlap Discrete Wavelet Transform (MODWT) and Hilbert transform. • The algorithm to classify normal fundamental heart sounds and abnormal additional lub/dub sounds in the systole or diastole intervals of a cardiac cycle, achieved an average SE of 89.15%, P+ of 89.71%, F1 of 89.41%, and CA of 95.11% using the test dataset from the PASCAL database. The top 10 features that achieved the highest weights in classifying these recordings were also identified. • Normal and abnormal classification of recordings using the proposed algorithm achieved a mean CA of 94.172%, and SE of 92.38%, in classifying recordings from the different databases. Among the top 10 acoustic features identified, the deterministic energy of the sound peaks of interest and the instantaneous frequency extracted using the Hilbert Huang-transform, achieved the highest weights. • The machine learning-based approach proposed to classify recordings of heart valve disorders (AS, MS, MR, and MVP) achieved an average CA of 98.26% and SE of 95.83%. 99 acoustic features were extracted and their abilities to differentiate these abnormalities were examined using weights obtained from the neighborhood component analysis (NCA). The top 10 features which showed the greatest abilities in classifying these abnormalities using recordings from the different databases were also identified. The achieved results demonstrate the ability of the algorithms to automatically identify and classify cardiac sounds. This work provides the basis for measurements of many useful clinical attributes of cardiac acoustic signals and can potentially help in monitoring the overall cardiac health for longer duration. The work presented in this thesis is the first-of-its-kind to validate the results using both, normal and pathological cardiac acoustic signals, recorded for a long continuous duration of 5 minutes at four different auscultation sites in non-controlled real-world conditions.Open Acces