AuthorAgyo, Sanfo D.
KeywordPhase space methods; Coherent states; Bi-fractional coherent states; Bi-fractional Wigner function; Bi-fractional P−function; Bi-fractional Q−function; Bi-fractional Moyal star product; Bi-fractional Berezin formalism
The University of Bradford theses are licenced under a Creative Commons Licence.
InstitutionUniversity of Bradford
DepartmentFaculty of Engineering and Informatics, School of Electrical Engineering and Computer Science
MetadataShow full item record
AbstractThe displacement operator is related to the displaced parity operator through a two dimensional Fourier transform. Both operators are important operators in phase space and the trace of both with respect to the density operator gives the Wigner functions (displaced parity operator) and Weyl functions (displacement operator). The generalisation of the parity-displacement operator relationship considered here is called the bi-fractional displacement operator, O(α, β; θα, θβ). Additionally, the bi-fractional displacement operators lead to the novel concept of bi-fractional coherent states. The generalisation from Fourier transform to fractional Fourier transform can be applied to other phase space functions. The case of the Wigner-Weyl function is considered and a generalisation is given, which is called the bi-fractional Wigner functions, H(α, β; θα, θβ). Furthermore, the Q−function and P−function are also generalised to give the bi-fractional Q−functions and bi-fractional P−functions respectively. The generalisation is likewise applied to the Moyal star product and Berezin formalism for products of non-commutating operators. These are called the bi-fractional Moyal star product and bi-fractional Berezin formalism. Finally, analysis, applications and implications of these bi-fractional transforms to the Heisenberg uncertainty principle, photon statistics and future applications are discussed.
Showing items related by title, author, creator and subject.
Novel Fractional Wavelet Transform with Closed-Form ExpressionAnoh, Kelvin O.O.; Abd-Alhameed, Raed A.; Jones, Steven M.R.; Ochonogor, O.; Dama, Yousef A.S. (2014-08)A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown.
Advanced MIMO-OFDM technique for future high speed braodband wireless communications. A study of OFDM design, using wavelet transform, fractional fourier transform, fast fourier transform, doppler effect, space-time coding for multiple input, multiple output wireless communications systemsAbd-Alhameed, Raed A.; Jones, Steven M.R.; Anoh, Kelvin O.O. (University of BradfordSchool of Engineering and Informatics, 2015)This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.
Buddlejol, a new alpha-chymotrypsin inhibitor from Buddleja asiaticaKhan, F.A.; Khan, N.M.; Khan, H.U.; Khan, S.; Ali, N.; Ahmad, S.; Maitland, Derek J. (2015)Buddlejol (1), a new sterol, has been isolated from the ethyl acetate soluble fraction of the antispasmodic plant Buddleja asiatica along with stigmasterol (2), lignoceric acid (3), taraxerol (4) and alpha-amyrin (5), respectively. The structure of Buddlejol (1) was established as (24S)-stigmast-5,22-diene-7 beta-ethoxy-3 beta-ol by spectral analysis and comparison with closely related structures. Buddlejol revealed to be a competitive inhibitor of chymotrypsin with the Ki value of 10.60 A mu M as indicated by Lineweaver-Burk and Dixon plots and their re-plots against its chymotrypsin inhibition assay, while the other compounds showed less inhibitory potential. The bioassay-guided isolation was stimulated by the preliminary cytotoxic screening of various fractions of B. asiatica.