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.

¡@¡@A single chip of variable length FFT processor is presented in this thesis. This processor can be applied for the applications with 128/256/512/1024/2048-point FFT. This processor is based on SDF (single path delay feedback) pipeline architecture with radix-2^3 computation element. The number of bits for input data and twiddle factors is carefully selected by system simulation to meet the requirements of OFDM system. In addition, we propose a feedback twiddle factor generator to instead the lookup table for twiddle factors to reduce the storage size of memory. The FFT processor is carried out by CMOS 0.35£gm 2P4M process with core area 3.381x3.3625 mm^2. In the gate level simulation, the output data rate of this FFT processor is above 22.72MHz, so the processor can meet the requirement of IEEE 802.16e standard.

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

International Telemetering Conference Proceedings / October 29-November 02, 1990 / Riviera Hotel and Convention Center, Las Vegas, Nevada / The Fast Fourier Transform (FFT) converts digitally sampled time domain data into the frequency domain. This paper will provide an advanced introduction for the telemetry engineer to basic FFT theory and then present and explain the different user preprocessing options that are available when using the FFT. These options include: using windowing functions, “zero filling” for frequency data interpolation, and setting the frequency resolution of the FFT resultant spectrum,

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / In many signal processing and telemetry applications only a portion of the Discrete Fourier Transform (DFT) of a data sequence is of interest. This paper develops an algorithm which enables computation of the FFT only over the frequency values of interest, reducing the computational complexity. As will be shown, the algorithm is also very modular which lends to efficient parallel processing implementation. This paper will begin by developing the frequency selective FFT algorithm, and conclude with a comparative analysis of the computational complexity of the algorithm with respect to the traditional FFT.

The ocean and acoustic modeling community has specifically asked for roughness from bathymetry. An effort has been undertaken to provide what can be thought of as the high frequency content of bathymetry. By contrast, the low frequency content of bathymetry is the set of contours. The two-dimensional amplitude spectrum calculated with the nonequispaced fast Fourier transform (Kunis, 2006) is exploited as the statistic to provide several parameters of roughness following the method of Fox (1996). When an area is uniformly rough, it is termed isotropically rough. When an area exhibits lineation effects (like in a trough or a ridge line in the bathymetry), the term anisotropically rough is used. A predominant spatial azimuth of lineation summarizes anisotropic roughness. The power law model fit produces a roll-off parameter that also provides insight into the roughness of the area. These four parameters give rise to several derived parameters. Algorithmic accomplishments include reviving Fox’s method (1985, 1996) and improving the method with the possibly geophysically more appropriate nonequispaced fast Fourier transform. A new composite parameter, simply the overall integral length of the nonlinear parameterizing function, is used to make within-dataset comparisons. A synthetic dataset and six multibeam datasets covering practically all depth regimes have been analyzed with the tools that have been developed. Data specific contributions include possibly discovering an aspect ratio isotropic cutoff level (less than 1.2), showing a range of spectral fall-off values between about -0.5 for a sandy- bottomed Gulf of Mexico area, to about -1.8 for a coral reef area just outside of the Saipan harbor. We also rank the targeted type of dataset, the best resolution gridded datasets, from smoothest to roughest using a factor based on the kernel dimensions, a percentage from the windowing operation, all multiplied by the overall integration length.

The following thesis applies an experimental design framework to investigate properties of electron transfer kinetics and homogeneous catalytic reactions. The approach is model-based and the classical Butler-Volmer description is chosen to describe the fundamental electrochemical reaction at a conductive interface. The methodology focuses on two significant design variables: the applied potential at the electrode and mass transport mode induced by physical arrangement. An important problem in electrochemistry is the recovery of model parameters from output current measurements. In this work, the identifiability function is proposed as a measure of correspondence between the parameters and output variable. Under diffusion-limit conditions, plain Monte Carlo optimization shows that the function is globally non-identifiable, or equivalently the correspondence is generally non-unique. However by selecting linear voltammetry as the applied potential, the primary parameters in the Butler-Volmer description are theoretically recovered from a single set of data. The result is accomplished via applications of Sobol ranking to reduce the parameter set and a sensitivity equation to inverse these parameters. The use of hydrodynamic tools for investigating electron transfer reactions is next considered. The work initially focuses on the rotating disk and its generalization - the rocking disk mechanism. A numerical framework is developed to analyze the latter, most notably the derivation of a Levich-like expression for the limiting current. The results are then used to compute corresponding identifiability functions for each of the above configurations. Potential effectiveness of each device in recovering kinetic parameters are straightforwardly evaluated by comparing the functional values. Furthermore, another hydrodynamic device - the rotating drum, which is highly suitable for viscous and resistive solvents, is theoretically analyzed. Combined with previous results, this rotating drum configuration shows promising potential as an alternative tool to traditional electrode arrangement. The final chapter illustrates the combination of modulated input signal and appro- priate mass transport regimes to express electro-catalytic effects. An AC voltammetry technique plays an important role in this approach and is discussed step-by-step from simple redox reaction to the complete EC′ catalytic mechanism. A general algorithm based on forward and inverse Fourier transform functions for extracting harmonic currents from the total current is presented. The catalytic effect is evaluated and compared for three cases: macro, micro electrodes under diffusion control condition and in micro fluidic environments. Experimental data are also included to support the simulated design results.

Visual inspection is the current method for determining if a wire rope needs to be removed from service. It can be time consuming and inaccurate. The point of this research is to prove that vibration testing could be used on rope to find damage. For this research, capacitive accelerometers were used. A program ran a Fast Fourier Transform (FFT) as the main analysis. From the data produced, it was determined that a damaged rope's vibration signature was different from the vibration signature of the undamaged rope. There were four different types of vibrations used: an impulse while measuring the axial response, a harmonic excitation while measuring the axial response and both transverses directions. The impulse did not provide consistent results to adequately find damage with an acceptable degree of confidence. The harmonic excitations did provide results that showed a different signature. This was the case for all three directions measured. As a result, it was determined that vibrations can be used to find damage in a wire rope.

Spherical means are a widespread model in modern imaging modalities like photoacoustic tomography. We develop Fourier based algorithms for an efficient computation of mean values. Furthermore we consider iterative reconstruction schemes, where we employ different regularization techniques.