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University of Macau / Faculty of Science and Technology / Department of Electrical and Computer Engineering

Several adaptive filters were investigated to enhance speech auditory brainstem responses (speech ABR). The objective was to shorten the long recording time currently needed by the standard coherent averaging method to obtain acceptable performance, which has limited the clinical adoption of speech ABR. Five algorithms were implemented: Wiener Filter (WF), Steepest Descent (SD), Adaptive Noise Cancellation (ANC) based on Least-Mean-Square error (LMS) and normalized LMS error (nLMS), and a multi-adaptive cascade combination of SD and LMS. The performance of the adaptive filters was assessed on speech ABR data gathered from several subjects and compared with coherent averaging using the overall Signal-to-Noise Ratio (SNR), the local SNR around the fundamental frequency and the first formant, and Mean-Square-Error (MSE) in the time and frequency domains. The adaptive filters could reduce the time needed, by at least one order of magnitude, for obtaining comparable signal quality as that obtained with coherent averaging.

The introduction of digital filtering is a new and exciting approach in analyzing in-situ seismic data. Digital filters are also in the same spirit as the electric cone which replaced the mechanical cone in CPT* testing. That is, it is desirable to automate CPT testing in order to make it less operator dependent and increase the reliability and accuracy. In CPT seismic cone testing seismic waves are generated at the surface and recorded downhole with velocity or acceleration transducers. The seismic receivers record the different seismic wavelets (e.g., SV-waves, P-waves) allowing one to determine shear and compression wave velocities. In order to distinguish the different seismic events, an instrument with fast response time is desired (i.e., high natural frequency and low damping). This type of instrument is characteristic of an accelerometer. The fast response time (small time constant) of an accelerometer results in a very sensitive instrument with corresponding noisy time domain characteristics. One way to separate events is to characterize the signal frequencies and remove unwanted frequencies. Digital filtering is ideal for this application. The techniques of digital filtering introduced in this research are based on frequency domain filtering, where Fast Fourier, Butterworth Filter, and crosscorrelation algorithms are implemented. One based on time domain techniques, where a Kalman Filter is designed to model'the instrument and the physical environment. The crosscorrelation method allows one to focus on a specific wavelet and use all the information of the wavelets present averaging out any noises or irregularities and relying upon dominant responses. The Kalman Filter was applied in a manner in which it modelled the sensors used and the physical environment of the body waves and noise generation. The KF was investigated for its possible application to obtaining accurate estimates on the P-wave and S-wave amplitudes and arrival times. The KF is a very flexible tool which allows one to model the problem considered accurately. In addition, the KF works in the time domain which removes many of the limitations of the frequency domain techniques. The crosscorrelation filter concepts are applied by a program referred to as CROSSCOR. CROSSCOR is a graphics interactive program which displays the frequency spectrums, unfiltered and filtered time series and crosscorrelations on a mainframe graphics terminal which has been adapted to run on the IBM P.C. CROSSCOR was tested for performance by analyzing synthetic and real data. The results from the analysis on both synthetic and real data indicate that CROSSCOR is an accurate and user friendly tool which greatly assists one in obtaining seismic velocities. The performance of the Kalman Filter was analyzed by generating a source wavelet and passing it through the second order instrumentation. The second order response is then fed into the KF with the arrival time and maximum amplitude being determined. The filter was found to perform well and it has much promise in respect that if it is finely turned, it would be possible to obtain arrival times and amplitudes on line resulting in velocities and damping characteristics, respectively. * Cone Penetration Test / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Thesis (M.Sc. (Mathematics)) -- University of Limpopo, 2021 / We study balanced filters and balanced z-filters considered by Carlson in [20] and [21] in topological spaces. We consider closed filters which are open-generated and open filters which are closed-generated. We show that a closed filter is open-generated precisely if it is a minimal balanced closed filter and that an open filter is closed-generated precisely when it is a minimal balanced open filter. For a completely regular topological space X, we study balanced z-filters and show that there is a one-to-one correspondence between the nonempty closed sets of βX and the balanced z-filter on X. By dualising closed filters we obtain ideals which then enables us to put some of the results in the context of frames. Dube in [28] has shown that a frame is normal if and only if its closed-generated filters are precisely the stably closed-generated ones. By dualisation we show that a frame is extremally disconnected if and only if its open-generated ideals are precisely the stably open-generated ones. We show that there is one-to-one correspondence between points of βL and the balanced ideals of Coz L. Furthermore we study nearness frames and show that the locally finite nearness frames strictly contain the Pervin nearness frames and the two coincide if the locally finite nearness frames are totally bounded. For perfect extension h : M → L of L, we show that a point p of M is a remote point if and only if Ip = {a ∈ L | h∗(a) ≤ p}. / University of Limpopo and DST - NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE - MaSS)

The ideal bandpass filter is defined as one which uniformly attenuates and delays all frequency components within the passband and effects zero transmission of all components outside the passband. For reasons which will be subsequently discussed, it is impossible to realize a stable lumped-element filter having this ideal characteristic. This has made it necessary to find ways to physically approximate such a characteristic. Some of the more widely used methods will be compared and analyzed in this paper.

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