Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis

The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose the novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal (FSAS) representations with following properties: (1) real part of eight FSAS representations is the original signal and imaginary part is the FCQT of the real part, (2) imaginary part of eight FSAS representations is the original signal and real part is the FSQT of the real part, (3) like the GAS, Fourier spectrum of the all FSAS representations has only positive frequencies, however unlike the GAS, the real and imaginary parts of the proposed FSAS representations are not orthogonal to each other. The Fourier decomposition method (FDM) is an adaptive data analysis approach to decompose a signal into a set of small number of Fourier intrinsic band functions which are AM-FM components. This study also proposes a new formulation of the FDM using the discrete cosine transform (DCT) with the GAS and FSAS representations, and demonstrate its efficacy for improved time-frequency-energy representation and analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure

Two-photon excitation spectroscopy of 1,5--Diphenyl-1,3,5-hexatriene using phase modulation

We have used two-photon Fourier transform spectroscopy to investigate the first singlet excited state (S1) of a prototypical polyene molecule 1,5 -- Diphenyl-1,3,5-hexatriene. As the S1 state in the polyenes is a one-photon forbidden transition, its structure of the vibrational levels cannot be studied using resonant linear excitation. Although this level is accessible with two-photon excitation, previous studies done by using wavelength tunable pulsed lasers did not have enough resolution to investigate the details of the vibrational levels. In Fourier transform spectroscopy, one uses a pair of laser beams to excite the sample. The measurements are done by varying the time delay between the pulses. The spectral resolution is given by the inverse of the maximum time delay rather than the spectral width of the pulses. We have used the method to investigate the vibrational levels of the S1 state. In our implementation, we have used a phase modulation technique to carry out the measurements in the rotating frame, which require fewer data points along the time delay thereby significantly reducing the measurement time

Haematological malignancy: are we measuring what is important to patients? A systematic review of quality of life instruments

© 2018 The Authors. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.The wide range of health‐related quality‐of‐life (HRQoL) instruments used in haematology makes it challenging for haematologists and other care team members in practice to select, use and understand the scoring system and finally interpret the results. The main objectives of this study were to: (a) provide a comprehensive list of quality‐of‐life issues important to patients suffering from haematological malignancies, identified through the literature; (b) provide a list of health‐related quality‐of‐life (HRQoL) instruments used in haematological malignancies in both daily clinical practice and research; and (c) evaluate the relevance and comprehensibility of the identified instruments in haematological malignancies. Systematic literature review of two databases, followed by addition of articles by manual searching, was carried out. The articles focusing on the primary studies, which have used semi‐structured/structured interviews or surveys to identify issues important to HM patients, and other studies describing the results of testing measurement properties, such as reliability, validity and responsiveness of the instruments currently used to evaluate the HRQoL in different HMs, were included. Fifty‐seven studies reported development and validation of 30 HRQoL instruments, which have been used in haematology. Twenty‐four studies were identified using qualitative methods to report HRQoL issues and symptoms from a patient's perspective. No identified instrument captured all the issues identified from the qualitative studies. None of the instruments reviewed appeared to have been developed for use in clinical practice and specifically for patients with HM, except MyPOS. Furthermore, measurement properties were established, largely, in clinical trial scenarios. There is a need for development of a new HRQoL instrument entirely based on involvement of patients with haematological malignancies.Peer reviewe