A Discrete Fourier Transform (DFT) changes the basis of a group algebra from the standard basis to a Fourier basis. An efficient application of a DFT is called a Fast Fourier Transform (FFT). This research pertains to a particular type of FFT called Decimation in Frequency (DIF). An efficient DIF has been established for commutative algebra; however, a successful analogue for non-commutative algebra has not been derived. However, we currently have a promising DIF algorithm for CSn called Orrison-DIF (ODIF). In this paper, I will formally introduce the ODIF and establish a bound on the operation count of the algorithm.

Recent work has shown that fast matrix multiplication algorithms can be constructed by embedding the two input matrices into a group algebra, applying a generalized discrete Fourier transform, and performing the multiplication in the Fourier basis. Developing an embedding that yields a matrix multiplication algorithm with running time faster than naive matrix multiplication leads to interesting combinatorial problems in group theory. The crux of such an embedding, after a group G has been chosen, lies in finding a triple of subsets of G that satisfy a certain algebraic relation. I show how the process of finding such subsets can in some cases be greatly simplified by considering the action of the group G on an appropriate set X. In particular, I focus on groups acting on regularly branching trees.

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The purpose of this work is to investigate the implementation of nitride fuels containing little or no uranium in a fast-spectrum nuclear reactor to reduce the amount of plutonium and minor actinides in spent nuclear fuel destined for the Yucca Mountain Repository. A two tier recycling strategy is proposed. Thermal spectrum transmutation systems converted from the existing LWR fleet were modeled for the first tier, and the Japanese fast reactor MONJU was used for the fast-spectrum transmutation. The modeling was performed with the Monteburns code. Transmutation performance was investigated as well as delayed neutron fraction, heat generation rates, and radioactivity of the spent material in the short and long term for the different transmutation fuel cycles. A two-tier recycling strategy incorporating fast and thermal transmutation with uranium-free nitride fuel was shown to reduce the long-term heat generation rates and radioactivity of the spent nuclear fuel inventory.

The purpose of this qualitative research, framed as a narrative inquiry, was to explore the experiences of a select familys participation in the Family and Schools Together (F&ST) program at an elementary school in Northwestern Saskatchewan. All members of this select family were Caucasian and of non-aboriginal descent. These participating family members, a mother, father and their three boys, told their story within the context of guided questions in the setting of individual unstructured interviews. The interviews were audio taped, transcribed, analyzed for unique and common threads and written into the form of a family narrative. Although unique threads were discovered from the analysis, the following common experiences emerged: the importance of taking time for family, the benefit of connecting with others and building relationships, the perception of the goals behind F&ST and favourite activities. These experiences were incorporated into the family narrative. <p>This study offers the opportunity for a greater awareness into the impact, participation in the F&ST (Family and Schools Together) intervention program has had on one select family and how that impact can be used to strengthen the delivery of that program and encourage others to get involved. Findings from this study show that the select family in this study experienced positive growth in family relationships, and positive affiliation with their school and community as a result of participating in F&ST. The findings from this study form the basis for implications for practice as well as for areas of further research.

No description available.

The purpose of this qualitative research, framed as a narrative inquiry, was to explore the experiences of a select familys participation in the Family and Schools Together (F&ST) program at an elementary school in Northwestern Saskatchewan. All members of this select family were Caucasian and of non-aboriginal descent. These participating family members, a mother, father and their three boys, told their story within the context of guided questions in the setting of individual unstructured interviews. The interviews were audio taped, transcribed, analyzed for unique and common threads and written into the form of a family narrative. Although unique threads were discovered from the analysis, the following common experiences emerged: the importance of taking time for family, the benefit of connecting with others and building relationships, the perception of the goals behind F&ST and favourite activities. These experiences were incorporated into the family narrative. <p>This study offers the opportunity for a greater awareness into the impact, participation in the F&ST (Family and Schools Together) intervention program has had on one select family and how that impact can be used to strengthen the delivery of that program and encourage others to get involved. Findings from this study show that the select family in this study experienced positive growth in family relationships, and positive affiliation with their school and community as a result of participating in F&ST. The findings from this study form the basis for implications for practice as well as for areas of further research.

In this thesis, an FFT (Fast Fourier Transform) hardware circuit is designed for OFDM systems. A new memory table permutation deletion method, which can reduce the size of memory storing twiddle factors table, is proposed. The architecture of the FFT circuit is based on the faster split-radix algorithm with SDF (Single-path Delay Feedback) pipeline structure. The bits number of the signal is carefully selected by system simulation to meet the system requirements. Based on the simulation results, a small area FFT circuit is carried out for OFDM systems.

In frequency-hopping (FH) system, the signal is not only impaired by receiver thermal noise, but also impaired by jamming, interference or multipath fading. Therefore, diversity techniques are used to reduce these impairments. Two systems are considered in this thesis, the first one is fast frequency-hopping/M-ary frequency-shift-keying (FFH/MFSK) System and the second one is fast frequency-hopping multiple access/M-ary frequency-shift-keying system (FFHMA/MFSK) System. In the first system, we consider three cases, multitone jamming (MTJ), broad-band noise jamming (BBN) and partial-band noise jamming (PBN).In the second system, we consider multiuser cases with multiple access interference, frequency-selective fading, and AWGN channels. In this thesis, two modified diversity combining methods are proposed. These methods are modified product and Order Statistics-Normalized Envelope Detection (OSNED) methods by adding the reliable order statistics. From simulation results, these methods can effectively combat multitone jamming and partial-band noise jamming. When comparing with product and OSNED in multiple access interference channel and frequency-selective fading channels, the proposed methods have better performance at high SNR. The proposed methods also do not need the additional side information as hard limiting majority vote (HLMV) and soft limiting combiner (SLC) needed.

Fast Fourier transformation (FFT) is a powerful analytical tool with wide-ranging applications in many fields. The standard FFT algorithms inherently assume that the length of the input and output sequence are equal. In practice, it is not always an accurate assumption. In certain case only some of the inputs to the transformation function are non-zero but lot of other are zero. In this thesis, a novel architecture of a 1024-point FFT, which adopts the transform decomposition (TD) algorithm, is presented to further reduce the complexity when the non-zero input data are consecutive. To implement this FFT processor, fixed point simulation is a conducted by using MATLB. The hardware implementation is realized by using the Verilog Hardware Description Language (HDL) which is taped out in TSMC0.18 Cell-Based Library for system verification.