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This project explores how to use band-pass filtering with a variety of filters to filter both two and three dimensional surface data. The software developed collects and makes available these filtering methods to support a larger project. It is used to automate the filtering procedure. This paper goes through the work-flow of the program, explaining how each filter was implemented. Then it demonstrates how the filters work by applying them to surface data used to test correlation between friction and roughness [Berglund and Rosen, 2009]. It also provides some explanations of the mathematical development of the filtering procedures as obtained from literature.

The first part of this thesis proposes a method to synthesize the T- and £S-prototype of band-pass filters using the two reflection zeros and the rolloff rate. According to the characteristics of passive components embedded in different substrates, £S-prototype band-pass filter is suitable for implementation on LTCC substrate, while T-prototype band-pass filter is suitable for implementation on organic substrate. The second part of this thesis employs the £S-prototype to design the LTCC band-pass filters. It has been found that mutual coupling and feedback elements can be used to create the multiple transmission zeros. With these synthesized transmission zeros, the stopband attenuation can be enhanced at several specific frequencies. For demonstration, this thesis implements the LTCC band-pass filters in 2.4 GHz ISM band and 3.5 GHz WiMAX band. The measured results show that insertion loss and return loss in the passband for these LTCC filters is less than 2 dB and more than 10 dB, respectively. In addition, these filters have the additional transmission zeros for enhancing the stopband attenuation. Moreover, miniaturization is also a key issue in implementing these LTCC filters. The 2.4 GHz and 3.5 GHz LTCC filter can meet the standard 1608 size and 2520 size, respectively, which are the smallest compared to the other LTCC filters reported for similar applications in the current literature and commercial media.

All-fiber multireflector spectral filters which have potential application in optical communications have been investigated experimentally. These multireflector etalons were produced by aligning equal-length fiber sections with TiO2/SiO2 dielectric mirrors deposited on the end in a silicon v-groove. Fiber sections 1.33mm in length were produced by polishing, with the fibers held in a silicon wafer polishing jig. The fibers were aligned inside the polishing jig using a precision micro positioner. Then four polishing steps with increasingly finer grit were applied to produce high-quality polished end surfaces on each fiber section. Finally, a dielectric mirror was deposited on one end of each fiber section by magnetron sputtering. After characterizing the optical loss, length, and mirror reflectance for each of the fiber sections, sections which were well-matched in length were chosen for assembly of the four-mirror etalon, which had nominal reflectance values of 10%, 50%, 50%, and 10% for the dielectric mirrors. Measured transmittance spectra for a mutireflector spectral filter were compared with calculated spectra. Thermal tuning of the multireflector etalon was also investigated. A 0.34 nm wavelength shift was observed for a 23° C temperature change, in agreement with prediction. increasingly finer grit were applied to produce high-quality polished end surfaces on each fiber section. Finally, a dielectric mirror was deposited on one end of each fiber section by magnetron sputtering. After characterizing the optical loss, length, and mirror reflectance for each of the fiber sections, sections which were well-matched in length were chosen for assembly of the four-mirror etalon, which had nominal reflectance values of 10%, 50%, 50%, and 10% for the dielectric mirrors. Measured transmittance spectra for a mutireflector spectral filter were compared with calculated spectra. Thermal tuning of the multireflector etalon was also investigated. A 0.34 nm wavelength shift was observed for a 23° C temperature change, in agreement with prediction.

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No / In this paper, a compact microstrip band-pass filter (BPF) covering the 3.4 to 3.8 GHz spectrum bandwidth for 5G wireless communications is presented. The planar filter uses three resonators, each terminated by a via to hole ground at one end and a capacitor at the other end with 50 Ω transmission line impedances for input and output terminals. The coupling between the lines is adjusted to resonate at the centre frequency with third-order band-pass Butterworth properties. The proposed combline filter is designed on an alumina substrate with a relative dielectric constant of 9.8 and a very small size of 9×5×1.2 mm3. The proposed filter is simulated and optimized using CST microwave studio software. / European Union’s Horizon 2020 research and innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET-722424, UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1

As a promising alternative to laboratory constrained video capture systems in studies of human movement, inertial sensors (accelerometers and gyroscopes) are recently gaining popularity. Secondary quantities such as velocity, displacement and joint angles can be calculated through integration of acceleration and angular velocities. However, it is broadly accepted that this procedure is significantly influenced by cumulative errors due to integration, arising from sensor noise, non-linearities, asymmetries, sensitivity variations and bias drifts. In this study, new methods for improving foot motion from inertial sensors are explored and assessed. / Sensor devices have been developed previously, for example, to detect postural changes that determine potential elderly fallers, and monitor a person’s gait. Recently, a gait variable known as minimum toe clearance (MTC) has been proposed to describe age-related declines in gait with better success as a predictor of falls risk. The MTC is the minimum vertical distance between the lowest point on the shoe and the ground during the mid-swing phase of the gait cycle. It is therefore of our interest to design a cost effective but accurate solution to measure toe clearance data which can then be used to identify the individuals at risk of falling. In this study, hardware, firmware and software features from off-the-shelf inertial sensors and wireless motes are evaluated and their configuration optimized for this application. A strap-down method, which consists of the minimizing of the integration drift due to cumulative errors, is evaluated off-line. Analysis revealed the necessity of band-pass filtering methods to correct systematic sensor errors that dramatically reduce the accuracy in estimating foot motion. / Cumulative errors were studied in the frequency domain, employing content of inertial sensor foot motion evaluated against a ’gold standard’ video-based device, namely the Optotrak Certus NDI. In addition, the effectiveness of applying band-pass filtering to raw inertial sensor data is assessed, under the assumption that sensor drift errors occur in the low frequency spectrum. The normalized correlation coefficient ρ of the Fast Fourier Transform (FFT) spectra corresponding to vertical toe acceleration from inertial sensors and from a video capture system as a function of digital band-pass filter parameters is compared. The Root Mean Square Error (RMSE) of the vertical toe displacement is calculated for 5 healthy subjects over a range of 4 walking speeds. The lowest RMSE and highest cross correlation achieved for the slowest walking speed of 2.5km/h was 3.06cmand 0.871 respectively, and 2.96cm and 0.952 for the fastest speed of 5.5km/h.

The n-solvable filtration of the link concordance group, defined by Cochran, Orr, and Teichner in 2003, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. We focus on the first two stages of the n-solvable filtration, which are the class of 0-solvable links and the class of 0.5-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric characterization 0-solve equivalent links. As a result, we completely characterize 0-solvable links and we give a classification of links up to 0-solve equivalence. We relate 0-solvable links to known results about links bounding gropes and Whitney towers in the 4-ball. We then establish a sufficient condition for a link to be 0.5-solvable and show that 0.5-solvable links must have vanishing Sato-Levine invariants.

This thesis realizes miniature bandpass filters using integrated passive device technology. The bandpass filters are designed based on coupled resonator method with single-band and dual-band responses, using a transformer structure with high-density winging pattern. In addition, the designs adopt the electric- and magnetic-field cancellation and the feedback mechanism to produce transmission zeros in the filter responses for enhancing selectivity and stopband rejection. In order to satisfy the specific requirements of commercial bandpass filter products, this thesis designed and implemented a trisection filter with cross coupling on a low-loss RT/Duroid substrate to generate a transmission zero very near the passband.

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