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    Design of a novel X-section architecture for FX-correlator in large interferometers : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering at Massey University, Auckland, New Zealand
    (Massey University, 2021) Balu, Vignesh Raja
    In large radio-interferometers it is considerably challenging to perform signal correlations at input data-rates of over 11 Tbps, which involves vast amount of storage, memory bandwidth and computational hardware. The primary objective of this research work is to focus on reducing the memory-access and design complexity in matrix architectural Big Data processing of the complex X-section of an FX-correlator employed in large array radio-telescopes. This thesis presents a dedicated correlator-system-multiplier-and -accumulator (CoSMAC) cell architecture based on the real input samples from antenna arrays which produces two 16-bit complex multiplications in the same clock cycle. The novel correlator cell optimization is achieved by utilizing the flipped mirror relationship between Discrete Fourier transform (DFT) samples owing to the symmetry and periodicity of the DFT coefficient vectors. The proposed CoSMAC structure is extended to build a new processing element (PE) which calculates both cross- correlation visibilities and auto-correlation functions simultaneously. Further, a novel mathematical model and a hardware design is derived to calculate two visibilities per baseline for the Quadrature signals (IQ sampled signals, where I is In-phase signal and Q is the 90 degrees phase shifted signal) named as Processing Element for IQ sampled signals (PE_IQ). These three proposed dedicated correlator cells minimise the number of visibility calculations in a baseline. The design methodology also targets the optimisation of the multiplier size in order to reduce the power and area further in the CoSMAC, PE and PE_IQ. Various fast and efficient multiplier algorithms are compared and combined to achieve a novel multiplier named Modified-Booth-Wallace-Multiplier and implemented in the CoSMAC and PE cells. The dedicated multiplier is designed to mostly target the area and power optimisations without degrading the performance. The conventional complex-multiplier-and-accumulators (CMACs) employed to perform the complex multiplications are replaced with these dedicated ASIC correlator cells along with the optimized multipliers to reduce the overall power and area requirements in a matrix correlator architecture. The proposed architecture lowers the number of ASIC processor cells required to calculate the overall baselines in an interferometer by eliminating the redundant cells. Hence the new matrix architectural minimization is very effective in reducing the hardware complexity by nearly 50% without affecting the overall speed and performance of very large interferometers like the Square Kilometre Array (SKA).
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    Real time multiple tau autocorrelator and its application in dynamic light scattering : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University
    (Massey University, 1996) Luo, Yi; Luo, Yi
    Dynamic light scattering (DLS) has recently been extended from a study of translational diffusion coefficients in dilute solution to a means of obtaining distributions in relaxation times over wide ranges of decay times. Many different data analysis algorithms have been developed to extract information on distribution functions (radius distribution, diffusion coefficient distribution, etc.) from photon correlation functions. Obtaining these distribution solutions usually involves the inversion of the Laplace Transform, and this can lead to ill-conditioned Fredholm integral equations of the first kind. These problems can be minimised by using an optimised time scale for the autocorrelation function. The need to handle such a dynamic range within one correlation function led to the development of the Multiple Tau Autocorrelator. This thesis describes the design and construction of a real time multiple tau autocorrelator and its application in DLS. An introduction to the theory of DLS is given. The theoretical background of the experiments is discussed and DLS techniques are reviewed. Particular emphasis is placed on experimental techniques and experimental data analysis procedures. The relationship among the intensity, amplitude, and photon count correlation functions are discussed. Data analysis methods based on obtaining distributions in relaxation times over wide ranges of decay times are discussed. Different hardware correlator system design techniques are reviewed. A correlator based on multiple tau techniques and symmetric normalisation is discussed. The advantages of using a multiple-instruction-multiple-data (MIMD) system to perform multiple tau autocorrelation is examined. The novel multiple digital signal processor (DSP) architecture for real time implementation of multiple tau autocorrelation is developed based on the task scheduling analysis, interconnection performance, and parallel processing. Detailed explanations of the operation of the Motorola DSP56001 digital signal processor are given, including architecture, addressing modes, instruction sets and peripheral access. The design and construction of the real time multiple tau autocorrelator is described. Detailed descriptions of hardware circuits and software are given. The correlator has proved satisfactory in its applications. The instrument can also works as spectrum analyser or other real time digital signal processing station. Two sets of experiments on ternary polymer solutions were carried out using the multiple tau correlator. The results of dynamic light scattering measurements are discussed within the broad framework of the Borsali-Benmouna theory. Experimental data are analysed using the constrained regularisation method. The interdiffusion coefficient and cooperative diffusion coefficient of PS/PMMA/thiophenol and PS/PMMA/toluene system under "optical tracer" conditions are discussed, and the interesting features of polymer polymer interaction as the temperature is varied are also discussed. Advantages of a multiple tau correlator over a linear correlator in the more complicated ternary polymer solution studies is demonstrated.