Analysis of the non-Markov parameter in continuous-time signal processing.

The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C(1) smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum.

On the dual structure of the auditory brainstem response in dogs.

OBJECTIVE: To use the over-complete discrete wavelet transform (OCDWT) to further examine the dual structure of auditory brainstem response (ABR) in the dog. METHODS: ABR waveforms recorded from 20 adult dogs at supra-threshold (90 and 70dBnHL) and threshold (0-15dBSL) levels were decomposed using a six level OCDWT and reconstructed at individual scales (frequency ranges) A6 (0-391Hz), D6 (391-781Hz), and D5 (781-1563Hz). RESULTS: At supra-threshold stimulus levels, the A6 scale (0-391Hz) showed a large amplitude waveform with its prominent wave corresponding in latency with ABR waves II/III; the D6 scale (391-781Hz) showed a small amplitude waveform with its first four waves corresponding in latency to ABR waves I, II/III, V, and VI; and the D5 scale (781-1563Hz) showed a large amplitude, multiple peaked waveform with its first six waves corresponding in latency to ABR waves I, II, III, IV, V, and VI. At threshold stimulus levels (0-15dBSL), the A6 scale (0-391Hz) continued to show a relatively large amplitude waveform, but both the D6 and D5 scales (391-781 and 781-1563Hz, respectively) now showed relatively small amplitude waveforms. CONCLUSIONS: A dual structure exists within the ABR of the dog, but its relative structure changes with stimulus level. SIGNIFICANCE: The ABR in the dog differs from that in the human both in the relative contributions made by its different frequency components, and the way these components change with stimulus level.

On wavelet analysis of auditory evoked potentials.

OBJECTIVE: To determine a preferred wavelet transform (WT) procedure for multi-resolution analysis (MRA) of auditory evoked potentials (AEP). METHODS: A number of WT algorithms, mother wavelets, and pre-processing techniques were examined by way of critical theoretical discussion followed by experimental testing of key points using real and simulated auditory brain-stem response (ABR) waveforms. Conclusions from these examinations were then tested on a normative ABR dataset. RESULTS: The results of the various experiments are reported in detail. CONCLUSIONS: Optimal AEP WT MRA is most likely to occur when an over-sampled discrete wavelet transformation (DWT) is used, utilising a smooth (regularity >or=3) and symmetrical (linear phase) mother wavelet, and a reflection boundary extension policy. SIGNIFICANCE: This study demonstrates the practical importance of, and explains how to minimize potential artefacts due to, 4 inter-related issues relevant to AEP WT MRA, namely shift variance, phase distortion, reconstruction smoothness, and boundary artefacts.

A wavelet visible difference predictor.

In this paper, we describe a model of the human visual system (HVS) based on the wavelet transform. This model is largely based on a previously proposed model, but has a number of modifications that make it more amenable to potential integration into a wavelet based image compression scheme. These modifications include the use of a separable wavelet transform instead of the cortex transform, the application of a wavelet contrast sensitivity function (CSF), and a simplified definition of subband contrast that allows one to predict the noise visibility directly from the wavelet coefficients. Initially, we outline the luminance, frequency, and masking sensitivities of the HVS and discuss how these can be incorporated into the wavelet transform. We then outline a number of limitations of the wavelet transform as a model of the HVS, namely the lack of translational invariance and poor orientation sensitivity. In order to investigate the efficacy of this wavelet based model, a wavelet visible difference predictor (WVDP) is described. The WVDP is then used to predict visible differences between an original and compressed (or noisy) image. Results are presented to emphasize the limitations of commonly used measures of image quality and to demonstrate the performance of the WVDP. The paper concludes with suggestions on how the WVDP can be used to determine a visually optimal quantization strategy for wavelet coefficients and produce a quantitative measure of image quality.

The performance of a variable-flow indirect calorimeter.

Indirect calorimetry estimates energy expenditure from measurement of respiratory gas exchange volumes. This paper considers the design and evaluation of an indirect calorimeter, the Europa GEM, suitable for use in nutritional research. The calorimeter is of the ventilated hood, flow-through type and is intended for use with spontaneously breathing patients. Our aim was to develop an accurate, flexible instrument with a high level of automation. Performance was assessed in a laboratory simulation using reference gas injections (n = 24) producing a mean error of 0.3 +/- 2% in oxygen consumption (VO2), 1.8 +/- 1% in carbon dioxide production (VCO2) and 1.4 +/- 1.5% in respiratory quotient (RQ). In order to investigate the effect of FeCO2 on error multiplication a further subdivision (n = 8) of tests at FeCO2 = 0.5%, 0.75% and 1% was made by modulating the air flow through the hood. However, the predicted increase in system accuracy with increasing FeCO2 was not apparent in practice.