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This paper presents technical foundations for a new technique of near-infrared transillumination-backscattering sounding, which is designed to enable noninvasive detection and monitoring of changes in the width of the subarachnoid space (SAS) and magnitude of cerebrovascular pulsation in humans. The key novelty of the technique is elimination of influence of blood flow in the scalp on the signals received from two infrared sensors-proximal and distal. A dedicated digital algorithm is used to estimate on line the ratio of the powers of received signals, referred to as two-sensor distal-to-proximal received power quotient, TQ (t). The propagation duct for NIR radiation reaching the distal sensor is the SAS filled with translucent cerebrospinal fluid. Information on slow fluctuations of the average width of the SAS is contained in the slow-variable part of the TQ (t), called the subcardiac component, and in TQ itself. Variations in frequency and magnitude of faster oscillations of the width of that space around the baseline value, dependent on cerebrovascular pulsation, are reflected in instantaneous frequency and envelope of the fast-variable component. Frequency and magnitude of the cerebrovascular pulsation depend on the action of the heart, so this fast-variable component is referred to as the cardiac component.

Abstract-The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature.

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