First Harmonic (2f) Characterisation of Resonant Frequency and Q-Factor of Micromechanical Transducers

In this paper, the response to the first harmonic component (2f) of the electrostatic force in single terminal driven electrostatic comb-drive and parallel-plate drive was used as a signal to extract device parameters, namely, the Q-factor and resonant frequency instead of the fundamental (1f) resonance response. It is shown that the difficulty in motional measurement due to electrical cross-talk (parasitics) using 1f measurement can be overcome with a higher signal-to-noise ratio of the 2f signal. Both atmospheric (low-Q) and reduced pressure environment were investigated using off-chip electronics and lock-in amplifier. The measurements were done on the electrostatic comb-drive and capacitive parallel plate sensing plates that form the two core modules of a yaw rate sensor (dual-axis resonator). The effects of AC and DC bias voltages on the measured response have been investigated. Experimental amplitude and phase response data have been analysed using the Lorentzian curve-fit, Resonance Curve Area (RCA) method, the half-power bandwidth method (3 dB) and the Nyquist plot for data fitting and determination of the Q-factor and resonance frequency.     

Configurable nonlinear filter generator

A configurable nonlinear filter generator is proposed. The nonlinear function employed is key controllable. By changing the key, a different sequence will be obtained. Simulated results show that an optimal linear complexity profile of the sequence can be generated     

Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry

A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction.     

Object boundary location by region and contour deformation

Many applications in image analysis need to distinguish an object from its surroundings. The `snake' method (Kass, 1987) is a well known method to solve such problems by locating the object boundary from an initial plan, but it has the limitation that the distance between the initial plan and the object boundary should be `very small'. The authors present a two-step method, which combines region and contour deformation, to locate the boundary of an object from a designated initial boundary plan. First, they propose a new deformable region model to represent an object, and use the model to locate the boundary of the object by region deformation. This step fills the gap between a fairly rough initial plan and the `snake' method. The resulting boundary is then used as the initial plan of a `snake' method to further refine the boundary. The results of the method are shown in simulated images and MRI images of brain tumour patients     

On a relation between information inequalities and group theory

We establish a one-to-one correspondence between information inequalities and group inequalities. The major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities, and vice versa. By giving a group-theoretic proof for all Shannon-type inequalities, we suggest that new inequalities could be discovered by making use of the rich set of tools in group theory. On the other hand, via a non-Shannon-type information inequality discovered by Zhang and Yeung (1997), we obtain a new inequality in group theory whose meaning is yet to be understood     

Simulation of a turbulent premixed open V-shaped flame using contour advection with surgery

Despite its capability of high spatial resolution, simulation of turbulent flows with traditional Lagrangian (front tracking) scheme is often discouraged by numerical instability caused by clustering of marker nodes and topological changes of fronts. Contour advection surgery (CAS), being a robust front tracking scheme, can limit the growth of front complexity during simulation without jeopardizing accuracy or efficiency. This allows it to open up an advantage over traditional front-tracking schemes. It has already been demonstrated that CAS, with incorporation of the reaction sheet model, can accurately simulate the propagation and advection of a turbulent premixed V-shaped flame. In this study, it is further tested with 10 values of vortex circulation. A range of upstream turbulence levels of 1.8–19.8% was obtained. Results indicate that upstream turbulence increase the average flame length, flame zone area and the overall burning rate. Flame surface density Σ was also estimated. Maximum values of Σ obtained lie in the range 0.1–1.4 mm⁻¹. Skewness towards the burnt region was observed in all profiles of Σ. Similar to results from laboratory experiments, it was found that Σ values decreases with upstream turbulence. From this study, the ability of CAS to cope with intense turbulence is demonstrated and a better quantitative understanding on the scheme has also been acquired.     

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.