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.

On-line induction machine condition monitoring techniques have been used widely in the detection of motor broken rotor bars for decades. Research has found that when broken bars occur in the machine rotor, the anomaly of electromagnetic field in the air gap will cause two sideband frequency components presenting in the stator current spectrum. Therefore, identification of these sideband frequencies can be used as a convenient and reliable approach to broken rotor bar fault diagnosis. Discrete Fourier Transform (DFT) is a conventional spectral analysis method used in this application. However, the use of DFT has several limitations. The most important one among them is the restriction of frequency resolution by window length. Due to this limitation, the accuracy of broken rotor bar detection can be highly affected in cases such as light machine load and limited data records. However, Prony's method for spectral analysis has the ability of overcoming the restriction of data window length on the frequency resolution, from which the DFT suffers. Such feature makes Prony's method a promising choice for broken rotor bar diagnosis when the machine is operating under light or varying load, or when only restricted data is available. In this thesis, I have demonstrated the implementation of this technique in the induction motor broken rotor bar detection, revealed its better performance than DFT in terms of maintaining high resolution in frequency domain whilst using a much shorter window, and analyzed the influential factors to the method of Prony Analysis (PA). In this thesis, an induction machine model that includes broken rotor bars is developed using Matlab/Simulink and verified by comparing the experimental and the simulated results. The Prony Analysis method for broken bar diagnosis is implemented and tested using both simulated and measured stator current data. Comparisons between PA and DFT results are presented, clearly indicating improvements of broken bar diagnostics using PA. / Thesis (M.Eng.Sc.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2008

Thesis (Ph. D.)--Texas Christian University, 2007. / Title from dissertation title page (viewed Dec. 10, 2007). Includes abstract. Includes bibliographical references.

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.

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.

Thesis (doctoral)--Georg-August-Universität zu Göttingen, 1919. / Cover title. Vita. Includes bibliographical references (p. [47]).

Thesis (M.S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / Dr. Feodor Vainstein, Committee Member; Dr. Doug Blough, Committee Chair; Dr. David Schimmel, Committee Member. Includes bibliographical references (leaves 71-75).

Thesis (M.S.)--Brigham Young University. Dept. of Computer Science, 2003. / Includes bibliographical references (p. 120-130).

The Cartesian Cubic lattice is known to be sub optimal when consideringband-limited signals but is still used as standard in three-dimensional medical magneticresonance imaging. The optimal sampling lattices are the body-centered cubic latticeand the face-centered cubic lattice. This report discusses the possible use of thesesampling lattices in MRI and presents verification of the non standard Fouriertransform method that is required for MR image creation for these sampling lattices.The results show that the Fourier transform is consistent with analytical models.

Let {Ij} be an interval partition of the integers, f(x) a function on the circle group T and S(f) = (sum |f j|2)1/2 where fˆ j = fˆ cIj . In their 1995 paper, Hare and Klemes showed that, for fixed p ∈ (1, infinity), there exist lambdap > 1 and Ap, Bp > 0 such that if l(Ij+1)/ l(Ij) ≥ lambdap, where l(Ij) is the length of the interval Ij, then Ap∥ f∥p ≤ ∥S( f)∥p ≤ Bp∥ f∥p. That is, {Ij} is a Littlewood-Paley (p) partition. Since the intervals need not be adjacent, these partitions may be viewed as permutations of lacunary intervals. Partitions like these can be induced by subsets of sums of permuted lacunary sequences. In this thesis, we present two main results. First, complementary to the aforementioned work of Hare and Klemes who proved that sums of permuted lacunary sequences were Littlewood-Paley (p) partitions (for large enough ratio), we prove the surprising result that there are sums of permuted lacunary sequences of fixed ratio that cannot be obtained by iterating sums of permuted lacunary sequences of larger ratio finitely many times. The proof of this statement is based on the ideas developed in the 1989 paper of Hare and Klemes, especially with respect to the definition of a tree and to the theorem on the equivalency of a finitely generated partition and the absence of certain trees. These special sums may then be viewed as the critical test case for further progress on the conjecture of Hare and Klemes that sums of permuted lacunary sequences are Littlewood-Paley (p) partitions for any p. Secondly, we use the non-branching case of the method of Hare and Klemes developed in their 1992 and 1995 papers, and further developed by Hare in a general setting in 1997, to prove a result of Marcinkiewicz on iterated lacunary sequences in the case p = 4. This shows that the method introduced by Hare and Klemes can potentially be adapted to partitions other than those they were originally applied to. As well, in considering the proof given by Hare and Klemes (and by Hare in a general setting) that lacunary sequences are Littlewood-Paley (4) partitions, we present a slight variation on one of the computations which may be useful in regard to sharp versions of some of these computations, but otherwise follows the same pattern as that of the above papers. Finally, we prove an elementary property of the finite union of lacunary sequences.