Two-dimensional anharmonic oscillator: application to 2,5-dihydrofuran

A program has been developed to calculate the energy levels and corresponding wavefunctions for a two‐dimensional anharmonic potential surface of at least C2v symmetry. This program has been employed to explain the high resolution splittings observed in the far infrared spectrum of 2,5‐dihydrofuran. The magnitude of the cross term connecting the ring‐twisting and ring‐puckering modes of 2,5‐dihydrofuran is sufficiently large to be significant. The potential surface determined also suggests that the ring‐twisting mode may be slightly anharmonic.

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Correcting for local oscillator phase offset in a DVB-T compliant receiver under multipath conditions

In 1997, the UK implemented the worlds first commercial digital terrestrial television system. Under the ETS 300 744 standard, the chosen modulation method, COFDM, is assumed to be multipath resilient. Previous work has shown that this is not necessarily the case. It has been shown that the local oscillator required for demodulation from intermediate-frequency to baseband must be very accurate. This paper shows that under multipath conditions, standard methods for obtaining local oscillator phase lock may not be adequate. This paper demonstrates a set of algorithms designed for use with a simple local oscillator circuit which will allow correction for local oscillator phase offset to maintain a low bit error rate with multipath present.

Local oscillator phase lock under multipath for video deghoster systems

Under multipath conditions, standard Video Intermediate Frequency (VIF) detectors generate a local oscillator phase error and consequently produce a dispersed non-ideal detected video signal due to the presence of additional IF carriers. The dispersed video causes problems when attempting to identify and remove the multipath interference, or ghosts, by the use of Digital Signal Processing and digital filtering. A digital phase lock system is presented which derives the correct phase for synchronous detection in the presence of multipath by using correlation information that has already been calculated as part of the deghosting process. As a result, the video deghoster system is made simpler, faster and more economical.

The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘a’ means ‘apple’”) is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, “3a + 2a = 5a” to year 7 pupils. Results included the notion that the ‘algebra as object’ analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not ‘supposed’ to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an‘algebra as object’ approach. Year 7 pupils did not explicitly refer to ‘algebra as object’, although some of their responses could be so interpreted. In the main, year 10 pupils used ‘algebra as object’ to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of ‘algebra as object’ in pupils’ thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.

Reduction of vestigial sideband effects due to multipath transmission in terrestrial broadcast television

In terrestrial television transmission multiple paths of various lengths can occur between the transmitter and the receiver. Such paths occur because of reflections from objects outside the direct transmission path. The multipath signals arriving at the receiver are all detected along with the intended signal causing time displaced replicas called 'ghosts' to appear on the television picture. With an increasing number of people living within built up areas, ghosting is becoming commonplace and therefore deghosting is becoming increasingly important. This thesis uses a deterministic time domain approach to deghosting, resulting in a simple solution to the problem of removing ghosts. A new video detector is presented which reduces the synchronous detector local oscillator phase error, caused by any practical size of ghost, to a lower level than has ever previously been achieved. From the new detector, dispersion of the video signal is minimised and a known closed-form time domain description of the individual ghost components within the detected video is subsequently obtained. Developed from mathematical descriptions of the detected video, a new specific deghoster filter structure is presented which is capable of removing both inphase (I) and also the phase quadrature (Q) induced ghost signals derived from the VSB operation. The new deghoster filter requires much less hardware than any previous deghoster which is capable of removing both I and Q ghost components. A new channel identification algorithm was also required and written which is based upon simple correlation techniques to find the delay and complex amplitude characteristics of individual ghosts. The result of the channel identification is then passed to the new I and Q deghoster filter for ghost cancellation. Generated from the research work performed for this thesis, five papers have been published. D

Implementation of Parallel (p,q) Counters for High Speed Digital Multipliers

Both the (5,3) counter and (2,2,3) counter multiplication techniques are investigated for the efficiency of their operation speed and the viability of the architectures when implemented in a fast bipolar ECL technology. The implementation of the counters in series-gated ECL and threshold logic are contrasted for speed, noise immunity and complexity, and are critically compared with the fastest practical design of a full-adder. A novel circuit technique to overcome the problems of needing high fan-in input weights in threshold circuits through the use of negative weighted inputs is presented. The authors conclude that a (2,2,3) counter based array multiplier implemented in series-gated ECL should enable a significant increase in speed over conventional full adder based array multipliers.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Analysis and compensation of I/Q imbalance in MIMO transmit-receive diversity systems

In wireless communication systems, all in-phase and quadrature-phase (I/Q) signal processing receivers face the problem of I/Q imbalance. In this paper, we investigate the effect of I/Q imbalance on the performance of multiple-input multiple-output (MIMO) maximal ratio combining (MRC) systems that perform the combining at the radio frequency (RF) level, thereby requiring only one RF chain. In order to perform the MIMO MRC, we propose a channel estimation algorithm that accounts for the I/Q imbalance. Moreover, a compensation algorithm for the I/Q imbalance in MIMO MRC systems is proposed, which first employs the least-squares (LS) rule to estimate the coefficients of the channel gain matrix, beamforming and combining weight vectors, and parameters of I/Q imbalance jointly, and then makes use of the received signal together with its conjugation to detect the transmitted signal. The performance of the MIMO MRC system under study is evaluated in terms of average symbol error probability (SEP), outage probability and ergodic capacity, which are derived considering transmission over Rayleigh fading channels. Numerical results are provided and show that the proposed compensation algorithm can efficiently mitigate the effect of I/Q imbalance.