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We hypothesized that blood lactate concentration([Lac]blood) is a function of cardiopulmonary variables, exercise intensity and some anthropometric elements during aerobic exercise. This investigation aimed to establish a mathematical model to estimate [Lac]blood noninvasively during constant work rate (CWR) exercise of various intensities. 31 healthy participants were recruited and each underwent 4 cardiopulmonary exercise tests: one incremental and three CWR tests (low: 35% of peak work rate for 15 min, moderate: 60% 10 min and high: 90% 4 min). At the end of each CWR test, venous blood was sampled to determine [Lac]blood. 31 trios of CWR tests were employed to construct the mathematical model, which utilized exponential regression combined with Taylor expansion. Good fitting was achieved when the conditions of low and moderate intensity were put in one model; high-intensity in another. Standard deviation of fitting error in the former condition is 0.52; in the latter is 1.82 mmol/liter. Weighting analysis demonstrated that, besides heart rate, respiratory variables are required in the estimation of [Lac]blood in the model of low/moderate intensity. In conclusion, by measuring noninvasive cardio-respiratory parameters, [Lac]blood during CWR exercise can be determined with good accuracy. This should have application in endurance training and future exercise industry.

We hypothesized that blood lactate concentration([Lac]blood) is a function of cardiopulmonary variables, exercise intensity and some anthropometric elements during aerobic exercise. This investigation aimed to establish a mathematical model to estimate [Lac]blood noninvasively during constant work rate (CWR) exercise of various intensities. 31 healthy participants were recruited and each underwent 4 cardiopulmonary exercise tests: one incremental and three CWR tests (low: 35% of peak work rate for 15 min, moderate: 60% 10 min and high: 90% 4 min). At the end of each CWR test, venous blood was sampled to determine [Lac]blood. 31 trios of CWR tests were employed to construct the mathematical model, which utilized exponential regression combined with Taylor expansion. Good fitting was achieved when the conditions of low and moderate intensity were put in one model; high-intensity in another. Standard deviation of fitting error in the former condition is 0.52; in the latter is 1.82 mmol/liter. Weighting analysis demonstrated that, besides heart rate, respiratory variables are required in the estimation of [Lac]blood in the model of low/moderate intensity. In conclusion, by measuring noninvasive cardio-respiratory parameters, [Lac]blood during CWR exercise can be determined with good accuracy. This should have application in endurance training and future exercise industry.

Deep networks, composed of multiple layers of hierarchical distributed representations, tend to learn low-level features in initial layers and transition to high-level features towards final layers. Paradigms such as transfer learning, multi-task learning, and continual learning leverage this notion of generic hierarchical distributed representations to share knowledge across datasets and tasks. Herein, we study the layer-wise transferability of representations in deep networks across a few datasets and tasks and note some interesting empirical observations., Comment: Accepted Paper in the Continual Learning Workshop, NeurIPS 2018

Jui-O Chen,1,2,* Jui-Fang Liu,1,3–5,* Yu-qi Liu,6 Yu-Mu Chen,7 Mei-Lien Tu,4 Hong-Ren Yu,8 Meng-Chih Lin,3,7 Chiu-Chu Lin,2 Shih-Feng Liu3,7 1Department of Nursing, Tajen University, Pingtung, Taiwan; 2College of Nursing, Kaohsiung Medical University, Kaohsiung, Taiwan; 3Department of Respiratory Therapy, Kaohsiung Chang Gung Memorial Hospital-Kaohsiung Medical Center and Chang Gung University College of Medicine, Kaohsiung, Taiwan; 4Respiratory Care, Chang Gung University of Science and Technology, Taoyuan, Taiwan; 5Department of Education, National Kaohsiung Normal University, Kaohsiung, Taiwan; 6Department of Intensive Care unit, The Second Affiliated Hospital of Fujian Medical University, Quanzhou, China; 7Division of Pulmonary and Critical Care Medicine, Department of Internal Medicine, Kaohsiung Chang Gung Memorial Hospital and Chang Gung University College of Medicine, Kaohsiung, Taiwan; 8Department of Pediatrics, Kaohsiung Chang Gung Memorial Hospital, Kaohsiung, Taiwan *These authors contributed equally to this work Purpose: It is unclear whether the effectiveness of pulmonary rehabilitation program (PRP) after cardiac surgery differs between patients with and without COPD. This study aimed to compare the effectiveness of PRP between patients with and without COPD undergoing coronary artery bypass graft (CABG) surgery. Patients and methods: We retrospectively included patients who underwent CABG surgery and received 3-week PRP from January 2009 to December 2013. We excluded patients who underwent emergency surgery, had an unstable hemodynamic status, were ventilator dependent or did not complete the PRP. Demographics, muscle strength, degree of dyspnea, pulmonary function and postoperative complications were compared. Results: Seventy-eight patients were enrolled (COPD group, n=40; non-COPD group, n=38). Maximal inspiratory pressure (MIP; −34.52 cmH2O vs −43.25 cmH2O, P<0.01; −34.67 cmH2O vs −48.18 cm

The selective oxidation of propane to acrylic acid is potential to replace the current manufacture of acrylic acid which uses propene as feedstock, due to this light alkane is more abundant and lower cost. Up to date, the most promising catalyst that has been reported for this selective oxidation of propane is MoVTeNbOx metal mixed oxide, yet its’ performance does not achieve the requirement of being commercialised. Thus, aseries of metal-promoted MoVTeNbOx catalysts (MVTN-A, where A = Co, Al, Mg) were synthesised by microwave-assisted slurry method, and then followed by calcination in air at 553 K for 1 hour and then in nitrogen at 873 K for 2 hours. It appears that the as-synthesised samples were semi-crystalline Anderson-type structure. Once calcined, the phase transformed into mixed phases of orthorhombic M1 phase, hexagonal M2 phase and tetragonal (V0.07Mo0.93)5O14 phase. Only when the samples were port-treated in hydrogen peroxide, the evolution of orthorhombic M1 phase was observed. Since there is no appreciable formation of orthorhombic M1 phase was obtained, the calcined catalysts were post-treated in 30 % hydrogen peroxide. The physicochemical properties of the catalysts were examined using X-ray Diffraction (XRD), Fourier-Transform Infrared (FT-IR), Brunauer-Emmett-Teller (BET) surface area measurement, Field Emission Scanning Electron Microscopy (FESEM) and Temperature Programmed Reduction in hydrogen (H2-TPR). Characteristics of the as-synthesised, calcined and post-treated catalysts were obtained. According to XRD results, highly pure orthorhombic M1 phase, Te2M20O57 (M = Mo, V or Nb), was formed when MoVTeNbOx was promoted with 0.06 mole of Mg, 0.02 mole of Al, or 0.10 mole of Al. An increase in specific surface area could be seen in those promoted with magnesium and aluminium, as compared to the un-promoted MoVTeNbOx (13.4 m2/g). On contrary, the specific surface area of cobalt-promoted catalysts was close to the un-promoted catalyst. Temperature Pro

The selective oxidation of propane to acrylic acid is potential to replace the current manufacture of acrylic acid which uses propene as feedstock, due to this light alkane is more abundant and lower cost. Up to date, the most promising catalyst that has been reported for this selective oxidation of propane is MoVTeNbOx metal mixed oxide, yet its’ performance does not achieve the requirement of being commercialised. Thus, aseries of metal-promoted MoVTeNbOx catalysts (MVTN-A, where A = Co, Al, Mg) were synthesised by microwave-assisted slurry method, and then followed by calcination in air at 553 K for 1 hour and then in nitrogen at 873 K for 2 hours. It appears that the as-synthesised samples were semi-crystalline Anderson-type structure. Once calcined, the phase transformed into mixed phases of orthorhombic M1 phase, hexagonal M2 phase and tetragonal (V0.07Mo0.93)5O14 phase. Only when the samples were port-treated in hydrogen peroxide, the evolution of orthorhombic M1 phase was observed. Since there is no appreciable formation of orthorhombic M1 phase was obtained, the calcined catalysts were post-treated in 30 % hydrogen peroxide. The physicochemical properties of the catalysts were examined using X-ray Diffraction (XRD), Fourier-Transform Infrared (FT-IR), Brunauer-Emmett-Teller (BET) surface area measurement, Field Emission Scanning Electron Microscopy (FESEM) and Temperature Programmed Reduction in hydrogen (H2-TPR). Characteristics of the as-synthesised, calcined and post-treated catalysts were obtained. According to XRD results, highly pure orthorhombic M1 phase, Te2M20O57 (M = Mo, V or Nb), was formed when MoVTeNbOx was promoted with 0.06 mole of Mg, 0.02 mole of Al, or 0.10 mole of Al. An increase in specific surface area could be seen in those promoted with magnesium and aluminium, as compared to the un-promoted MoVTeNbOx (13.4 m2/g). On contrary, the specific surface area of cobalt-promoted catalysts was close to the un-promoted catalyst. Temperature Pro

Infections by microorganisms are a major problem in public health throughout the world. Artificial materials, including biomedical goods, inherently lack defense against microbial development. Therefore, microbial cells can adhere on any type of artificial surface, particularly in a moist environment, and start to multiply to form a huge population. In this review, we will discuss a strategy for designing antimicrobial polymers and antimicrobial surfaces. Generally, there are five types of antimicrobial polymers: (a) polymeric biocides, (b) biocidal polymers, (c) biocide-releasing polymers, (d) bioactive oligopeptides, and (e) antimicrobial surfaces. Antimicrobial surfaces preventing the growth of microorganisms are a promising method to inhibit the spread of microbial infections. The antimicrobial surfaces can reject the attachment of microbes and/or kill microbes in the vicinity and can be designed to kill microbes on contact. It is recommended that the material surface not release biocidal substances, therefore preventing exhaustion of biocide release to kill microbes. Furthermore, the antimicrobial surfaces are desired to be nontoxic to human cells. The development of contact-active antimicrobial surfaces by grafting antimicrobial nanosegments onto the material surface will be an important topic in the future.

Infections by microorganisms are a major problem in public health throughout the world. Artificial materials, including biomedical goods, inherently lack defense against microbial development. Therefore, microbial cells can adhere on any type of artificial surface, particularly in a moist environment, and start to multiply to form a huge population. In this review, we will discuss a strategy for designing antimicrobial polymers and antimicrobial surfaces. Generally, there are five types of antimicrobial polymers: (a) polymeric biocides, (b) biocidal polymers, (c) biocide-releasing polymers, (d) bioactive oligopeptides, and (e) antimicrobial surfaces. Antimicrobial surfaces preventing the growth of microorganisms are a promising method to inhibit the spread of microbial infections. The antimicrobial surfaces can reject the attachment of microbes and/or kill microbes in the vicinity and can be designed to kill microbes on contact. It is recommended that the material surface not release biocidal substances, therefore preventing exhaustion of biocide release to kill microbes. Furthermore, the antimicrobial surfaces are desired to be nontoxic to human cells. The development of contact-active antimicrobial surfaces by grafting antimicrobial nanosegments onto the material surface will be an important topic in the future.

The stem cell fates of pluripotency and differentiation are regulated by not only soluble biological cues but also insoluble biochemical cues (i.e., extracellular matrix (ECM)) and the physical cues of cell culture biomaterials (i.e., elasticity). We investigated the maintenance of pluripotency and the differentiation lineages of human amniotic fluid-derived stem cells (hAFSCs) cultured on poly(vinyl alcohol-co-itaconic acid) (PVA) hydrogels grafted with several types of ECM and corresponding oligopeptides in expansion medium. hAFSCs cultured on soft PVA hydrogels (12.2 kPa) that were grafted with oligopeptides derived from fibronectin and vitronectin showed high pluripotency, which was evaluated by Oct4, Sox2 and Nanog expression. The hAFSCs grown on soft PVA hydrogels (12.2 kPa) grafted with each oligopeptide showed higher pluripotency, as assessed by Oct4 and Nanog expression, than hAFSCs grown on stiff PVA hydrogels (25.3 kPa) grafted with the same oligopeptides and a much higher pluripotency than those grown on rigid tissue-culture polystyrene dishes. Soft biomaterials appeared to be adequate to maintain the pluripotency of hAFSCs. Surprisingly, hAFSCs that showed higher pluripotency on PVA hydrogels grafted with oligopeptides derived from fibronectin and vitronectin also expressed higher levels of early differentiation markers for three germ layers in expansion medium. This result suggests that hAFSCs are heterogeneous and that this population contains highly pluripotent stem cells and stem cells that can be easily differentiated.

The stem cell fates of pluripotency and differentiation are regulated by not only soluble biological cues but also insoluble biochemical cues (i.e., extracellular matrix (ECM)) and the physical cues of cell culture biomaterials (i.e., elasticity). We investigated the maintenance of pluripotency and the differentiation lineages of human amniotic fluid-derived stem cells (hAFSCs) cultured on poly(vinyl alcohol-co-itaconic acid) (PVA) hydrogels grafted with several types of ECM and corresponding oligopeptides in expansion medium. hAFSCs cultured on soft PVA hydrogels (12.2 kPa) that were grafted with oligopeptides derived from fibronectin and vitronectin showed high pluripotency, which was evaluated by Oct4, Sox2 and Nanog expression. The hAFSCs grown on soft PVA hydrogels (12.2 kPa) grafted with each oligopeptide showed higher pluripotency, as assessed by Oct4 and Nanog expression, than hAFSCs grown on stiff PVA hydrogels (25.3 kPa) grafted with the same oligopeptides and a much higher pluripotency than those grown on rigid tissue-culture polystyrene dishes. Soft biomaterials appeared to be adequate to maintain the pluripotency of hAFSCs. Surprisingly, hAFSCs that showed higher pluripotency on PVA hydrogels grafted with oligopeptides derived from fibronectin and vitronectin also expressed higher levels of early differentiation markers for three germ layers in expansion medium. This result suggests that hAFSCs are heterogeneous and that this population contains highly pluripotent stem cells and stem cells that can be easily differentiated.

In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) for multi-input single-output (MISO) interference channels (ICs) which is well acknowledged as general models of heterogeneous networks (HetNets), multicell networks, etc. To address this problem, we develop an efficient distributed beamforming algorithm based on a pricing mechanism. Specifically, we carefully introduce a price metric for distributed beamforming design which fortunately allows efficient closed-form solutions to the per-user beam-vector optimization problem. The convergence of the distributed pricing-based beamforming design is theoretically proven. Furthermore, we present an implementation strategy of the proposed distributed algorithm with limited information exchange. Numerical results show that our algorithm converges much faster than existing algorithms, while yielding comparable, sometimes even better performance in terms of the WS-EE. Finally, by taking the backhaul power consumption into account, it is interesting to show that the proposed algorithm with limited information exchange achieves better WS-EE than the full information exchange based algorithm in some special cases., Comment: 40 pages

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005., In title on t.p., superscript "TM" follows "S-3DP"., Includes bibliographical references., GRIN lenses with vertical index variation and radial index variation have been successfully fabricated using S-3DPTM. Two silica-based material systems, A1203-SiO₂ and BaO-SiO₂, have been studied and used for the fabrication of GRIN lenses. Aluminum nitrate was dissolved in water to provide the dopant salt solution for S-3DPTM. The pre-sintering treatment at 1000 ⁰Cfor 24 hours in. vacuum (-5x10-6 torr) was used to remove the hydroxyl groups that cause bubbles during sintering. The sintering condition for the A1203-SiO₂ material system was found to be 1650 ⁰C for 30 minutes in vacuum. Two alumina-doped silica GRIN lenses with vertical index variation, Design 1.63 [percent] max and Design 2.5 [percent] max, were fabricated with effective focal lengths of 10.00 cm and 6.10 cm, respectively. An alumina-doped silica GRIN lens with radial parabolic index variation also was fabricated with effective focal lengths of 63.75 cm in the x direction and 52.50 cm in the y direction. The BaO-SiO₂ material system, which has a 2.4 stronger index changing ability than the A1203-SiO₂ material system, also was developed. Barium acetate was used as the dopant source. The pre-sintering treatment was found to be 900 ⁰C for 18 hours in air to convert barium acetate to barium oxide. The sintering condition was found to be 1725 ⁰C for 10 minutes in vacuum. A barium oxide-doped GRIN lens with radial parabolic index variation was fabricated. Its effective focal length was measured to be 14.63 cm in the x direction and 11.14 cm in the y direction. The barium oxide concentration profiles were measured. The theoretical focal lengths were calculated and compared with the effective focal lengths., by Hong-Ren Wang., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005., In title on t.p., superscript "TM" follows "S-3DP"., Includes bibliographical references., GRIN lenses with vertical index variation and radial index variation have been successfully fabricated using S-3DPTM. Two silica-based material systems, A1203-SiO₂ and BaO-SiO₂, have been studied and used for the fabrication of GRIN lenses. Aluminum nitrate was dissolved in water to provide the dopant salt solution for S-3DPTM. The pre-sintering treatment at 1000 ⁰Cfor 24 hours in. vacuum (-5x10-6 torr) was used to remove the hydroxyl groups that cause bubbles during sintering. The sintering condition for the A1203-SiO₂ material system was found to be 1650 ⁰C for 30 minutes in vacuum. Two alumina-doped silica GRIN lenses with vertical index variation, Design 1.63 [percent] max and Design 2.5 [percent] max, were fabricated with effective focal lengths of 10.00 cm and 6.10 cm, respectively. An alumina-doped silica GRIN lens with radial parabolic index variation also was fabricated with effective focal lengths of 63.75 cm in the x direction and 52.50 cm in the y direction. The BaO-SiO₂ material system, which has a 2.4 stronger index changing ability than the A1203-SiO₂ material system, also was developed. Barium acetate was used as the dopant source. The pre-sintering treatment was found to be 900 ⁰C for 18 hours in air to convert barium acetate to barium oxide. The sintering condition was found to be 1725 ⁰C for 10 minutes in vacuum. A barium oxide-doped GRIN lens with radial parabolic index variation was fabricated. Its effective focal length was measured to be 14.63 cm in the x direction and 11.14 cm in the y direction. The barium oxide concentration profiles were measured. The theoretical focal lengths were calculated and compared with the effective focal lengths., by Hong-Ren Wang., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005., In title on t.p., superscript "TM" follows "S-3DP"., Includes bibliographical references., GRIN lenses with vertical index variation and radial index variation have been successfully fabricated using S-3DPTM. Two silica-based material systems, A1203-SiO₂ and BaO-SiO₂, have been studied and used for the fabrication of GRIN lenses. Aluminum nitrate was dissolved in water to provide the dopant salt solution for S-3DPTM. The pre-sintering treatment at 1000 ⁰Cfor 24 hours in. vacuum (-5x10-6 torr) was used to remove the hydroxyl groups that cause bubbles during sintering. The sintering condition for the A1203-SiO₂ material system was found to be 1650 ⁰C for 30 minutes in vacuum. Two alumina-doped silica GRIN lenses with vertical index variation, Design 1.63 [percent] max and Design 2.5 [percent] max, were fabricated with effective focal lengths of 10.00 cm and 6.10 cm, respectively. An alumina-doped silica GRIN lens with radial parabolic index variation also was fabricated with effective focal lengths of 63.75 cm in the x direction and 52.50 cm in the y direction. The BaO-SiO₂ material system, which has a 2.4 stronger index changing ability than the A1203-SiO₂ material system, also was developed. Barium acetate was used as the dopant source. The pre-sintering treatment was found to be 900 ⁰C for 18 hours in air to convert barium acetate to barium oxide. The sintering condition was found to be 1725 ⁰C for 10 minutes in vacuum. A barium oxide-doped GRIN lens with radial parabolic index variation was fabricated. Its effective focal length was measured to be 14.63 cm in the x direction and 11.14 cm in the y direction. The barium oxide concentration profiles were measured. The theoretical focal lengths were calculated and compared with the effective focal lengths., by Hong-Ren Wang., Ph.D.

The traditional Slurry-based Three-dimensional Printing (S-3DP(TM)) process has been used to fabricate complex structure materials by printing organic binders in selected positions on each printing layer. This process is modified to fabricate functional graded materials, such as gradient index (GRIN) lenses, by depositing different concentrations of dopant at different positions. The modified S-3DP(TM) process offers advantages over conventional GRIN lens processes, including reduced processing time, improved compositional flexibility, and increased index profile dimensionality. Two different approximately parabolic dopant concentration profiles, which have maximum alumina concentrations of 1.63 mol% and 2.50 mol%, are printed into silica powder beds using S-3DP(TM). The samples with maximum alumina concentration of 1.63 mol% have been sintered into optical transparency at 1650 deg. C for 30 minutes in a vacuum furnace (5x10(exp -6) torr) while an additional dehydration process before sintering was required for the samples with maximum alumina concentration of 2.50 mol%. The magnifying effects of GRIN lenses with profiles of 1.63 mol% and 2.50 mol% alumina were observed, yielding effective focal lengths of 10 cm and 6.1 cm, respectively. Light diffraction, which results from the locally inhomogeneous dopant distribution and reduces the optical quality of GRIN lenses, was also observed., This article is from the Mat. Res. Soc. Symp. Proc. Vol. 758 p35-40, 2003. This article is from ADA417756 Materials Research Society Symposium Proceedings, Volume 758 Held in Boston, Massachusetts on December 3-5, 2002. Rapid Prototyping Technologies

Two important convergence properties of Lyapunov-theory-based adaptive filtering (LAF) adaptive filters are first explored. The LAF finite impulse response and infinite impulse response adaptive filters are then realized using the radial basis function (RBF) neural networks (NNs). The proposed adaptive RBF neural filtering system possesses the distinctive properties of RBF NN and the LAF filtering system. Unlike many adaptive filtering schemes using gradient search techniques, a Lyapunov function of the error between the desired signal and the RBF NN output is first defined. By properly choosing the weights update law in the Lyapunov sense, the RBF filter output can asymptotically converge to the desired signal. The design is independent of the stochastic properties of the input disturbances and the stability is guaranteed by the Lyapunov stability theory. Simulation examples for nonlinear adaptive prediction of nonstationary signal and system identification are performed.

A structural approach to the construction of multidimensional vector radix fast Discrete Fourier Transforms (DFTs) and fast direct Discrete Cosine Transforms (DCTs) is presented in this thesis. The approach features the use of matrix representation (1-D) and two-dimensional (2-D) FFT and fast DCT algorithms along with the tensor product, and the use of logic diagram and rules for modifications. In the first part of the thesis, the structural approach is applied to construct 2-D Decimation-In-Time (DIT), Decimation-In-Frequency (DIF) and mixed (DIT & DIF) vector radix FFT algorithms from corresponding 1-D FFT algorithms by the Cooley- Tukey method. The results are summarized in theorems as well as examples using logic diagrams. It has been shown that the logic diagram (or signal flow graph) as well as being a form of representation and interpretation of fast algorithm equations, is a engineering tool for the construction of fast algorithms. The concept of "vector signal processing" is adapted into the logic diagram representation which reveals the structural features of multidimensional vector radix FFTs and explains the relationships and differences between the row-column FFT, the vector radix FFT reported previously and the approach presented in this thesis. The introduction of the structural approach makes the formulation of a multidimensional vector radix FFT algorithm of high radix dimension easy to evaluate and implement by both software and hardware. The hardware implementation of 2-D DFTs is discussed in the light of vector radix FFTs using the Frequency Domain Processor (FDP™) A41102, which has shown improvement in reducing the system complexity over the traditional row-column method. With the help of the structural approach, the vector split-radix DIF FFT algorithm, mixed (DIT & DIF) vector radix FFT and Combined Factor (CF) vector radix FFT algorithms are presented whereby a comparison study is made in terms of arithmetic complexity. The approach is then g

A structural approach to the construction of multidimensional vector radix fast Discrete Fourier Transforms (DFTs) and fast direct Discrete Cosine Transforms (DCTs) is presented in this thesis. The approach features the use of matrix representation (1-D) and two-dimensional (2-D) FFT and fast DCT algorithms along with the tensor product, and the use of logic diagram and rules for modifications. In the first part of the thesis, the structural approach is applied to construct 2-D Decimation-In-Time (DIT), Decimation-In-Frequency (DIF) and mixed (DIT & DIF) vector radix FFT algorithms from corresponding 1-D FFT algorithms by the Cooley- Tukey method. The results are summarized in theorems as well as examples using logic diagrams. It has been shown that the logic diagram (or signal flow graph) as well as being a form of representation and interpretation of fast algorithm equations, is a engineering tool for the construction of fast algorithms. The concept of "vector signal processing" is adapted into the logic diagram representation which reveals the structural features of multidimensional vector radix FFTs and explains the relationships and differences between the row-column FFT, the vector radix FFT reported previously and the approach presented in this thesis. The introduction of the structural approach makes the formulation of a multidimensional vector radix FFT algorithm of high radix dimension easy to evaluate and implement by both software and hardware. The hardware implementation of 2-D DFTs is discussed in the light of vector radix FFTs using the Frequency Domain Processor (FDP™) A41102, which has shown improvement in reducing the system complexity over the traditional row-column method. With the help of the structural approach, the vector split-radix DIF FFT algorithm, mixed (DIT & DIF) vector radix FFT and Combined Factor (CF) vector radix FFT algorithms are presented whereby a comparison study is made in terms of arithmetic complexity. The approach is then g

A structural approach to the construction of multidimensional vector radix fast Discrete Fourier Transforms (DFTs) and fast direct Discrete Cosine Transforms (DCTs) is presented in this thesis. The approach features the use of matrix representation (1-D) and two-dimensional (2-D) FFT and fast DCT algorithms along with the tensor product, and the use of logic diagram and rules for modifications. In the first part of the thesis, the structural approach is applied to construct 2-D Decimation-In-Time (DIT), Decimation-In-Frequency (DIF) and mixed (DIT & DIF) vector radix FFT algorithms from corresponding 1-D FFT algorithms by the Cooley- Tukey method. The results are summarized in theorems as well as examples using logic diagrams. It has been shown that the logic diagram (or signal flow graph) as well as being a form of representation and interpretation of fast algorithm equations, is a engineering tool for the construction of fast algorithms. The concept of "vector signal processing" is adapted into the logic diagram representation which reveals the structural features of multidimensional vector radix FFTs and explains the relationships and differences between the row-column FFT, the vector radix FFT reported previously and the approach presented in this thesis. The introduction of the structural approach makes the formulation of a multidimensional vector radix FFT algorithm of high radix dimension easy to evaluate and implement by both software and hardware. The hardware implementation of 2-D DFTs is discussed in the light of vector radix FFTs using the Frequency Domain Processor (FDP™) A41102, which has shown improvement in reducing the system complexity over the traditional row-column method. With the help of the structural approach, the vector split-radix DIF FFT algorithm, mixed (DIT & DIF) vector radix FFT and Combined Factor (CF) vector radix FFT algorithms are presented whereby a comparison study is made in terms of arithmetic complexity. The approach is then g