Dissertations / Theses on the topic 'Discrete Fourier transforms (DFTs)'
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Heiskanen, Andreas, and Erik Johansson. "Analysing Memory Performance when computing DFTs using FFTW." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-230225.
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Discrete Fourier Transforms (DFTs) are used in a wide variety of dif-ferent scientific areas. In addition, there is an ever increasing demand on fast and effective ways of computing DFT problems with large data sets. The FFTW library is one of the most common used libraries when computing DFTs. It adapts to the system architecture and predicts the most effective way of solving the input problem. Previous studies have proved the FFTW library to be superior to other DFT solving libraries. However, not many have specifically examined the cache memory performance, which is a key factor for overall performance. In this study, we examined the cache memory utilization when computing 1-D complex DFTs using the FFTW library. Testing was done using bench FFT, Linux Perf and testing scripts. The results from this study show that cache miss ratio increases with problem size when the input size is smaller than the theoretical input size matching the cache capacity. This is also verified by the results from the L2 prefetcher miss ratio. However, the study show that cache miss ratio stabilizes when exceeding the cache capacity. In conclusion, it is possible to use bench FFT and Linux Perf to measure cache memory utilization. Also, the analysis shows that cache memory performance is good when computing 1-D complex DFTS using the FFTW library, since the miss ratios stabilizes at low values. However, we suggest further examination ofthe memory behaviour for DFT computations using FFTW with larger input sizes and a more in-depth testing method.Diskret Fouriertransform (DFT) används inom många olika vetenskapliga områden. Det finns en ökande efterfrågan på snabba och effektiva sätt att beräkna DFT-problem med stora mängder data. FFTW-biblioteket är ett av de mest använda biblioteken vid beräkning av DFT-problem. FFTW-biblioteket anpassar sig till systemarkitekturen och försöker generera det mest effektiva sättet att lösa ett givet DFT-problem. Tidigare studier har visat att FFTW-biblioteket är effektivare än andra bibliotek som kan användas för att lösa DFT-problem. Däremot har studierna inte fokuserat på minneshanteringen, vilket är en nyckelfaktor för den generella prestandan. I den här studien undersökte vi FFTW-bibliotekets cache-minneshanteringen vid beräkning av 1-D komplexa DFT-problem. Tester utfördes med hjälp av bench FFT, Linux Perf och testskript. Resultaten från denna studie visar att cache-missförhållandet ökar med problemstorleken när problemstorleken ärmindre än den teoretiska problemstorleken som matchar cachekapaciteten. Detta bekräftas av resultat från L2-prefetcher-missförhållandet. Studien visar samtidigt att cache-missförhållandet stabiliseras när problemstorleken överskrider cachekapaciteten. Sammanfattningsvis går det att argumentera för att det är möjligt att använda bench FFT och Linux Perf för att mäta cache-minneshanteringen. Analysen visar också att cache-minneshanteringen är bra vid beräkning av 1-D komplexa DFTs med hjälp av FFTW-biblioteket eftersom missförhållandena stabiliseras vid låga värden. Vi föreslår dock ytterligare undersökning av minnesbeteendet för DFT-beräkningar med hjälp av FFTW där problemstorlekarna är större och en mer genomgående testmetod används.
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Akhtar, Mahmood Electrical Engineering & Telecommunications Faculty of Engineering UNSW. "Genomic sequence processing: gene finding in eukaryotes." Publisher:University of New South Wales. Electrical Engineering & Telecommunications, 2008. http://handle.unsw.edu.au/1959.4/40912.
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Of the many existing eukaryotic gene finding software programs, none are able to guarantee accurate identification of genomic protein coding regions and other biological signals central to pathway from DNA to the protein. Eukaryotic gene finding is difficult mainly due to noncontiguous and non-continuous nature of genes. Existing approaches are heavily dependent on the compositional statistics of the sequences they learn from and are not equally suitable for all types of sequences. This thesis firstly develops efficient digital signal processing-based methods for the identification of genomic protein coding regions, and then combines the optimum signal processing-based non-data-driven technique with an existing data-driven statistical method in a novel system demonstrating improved identification of acceptor splice sites. Most existing well-known DNA symbolic-to-numeric representations map the DNA information into three or four numerical sequences, potentially increasing the computational requirement of the sequence analyzer. Proposed mapping schemes, to be used for signal processing-based gene and exon prediction, incorporate DNA structural properties in the representation, in addition to reducing complexity in subsequent processing. A detailed comparison of all DNA representations, in terms of computational complexity and relative accuracy for the gene and exon prediction problem, reveals the newly proposed ?paired numeric? to be the best DNA representation. Existing signal processing-based techniques rely mostly on the period-3 behaviour of exons to obtain one dimensional gene and exon prediction features, and are not well equipped to capture the complementary properties of exonic / intronic regions and deal with the background noise in detection of exons at their nucleotide levels. These issues have been addressed in this thesis, by proposing six one-dimensional and three multi-dimensional signal processing-based gene and exon prediction features. All one-dimensional and multi-dimensional features have been evaluated using standard datasets such as Burset/Guigo1996, HMR195, and the GENSCAN test set. This is the first time that different gene and exon prediction features have been compared using substantial databases and using nucleotide-level metrics. Furthermore, the first investigation of the suitability of different window sizes for period-3 exon detection is performed. Finally, the optimum signal processing-based gene and exon prediction scheme from our evaluations is combined with a data-driven statistical technique for the recognition of acceptor splice sites. The proposed DSP-statistical hybrid is shown to achieve 43% reduction in false positives over WWAM, as used in GENSCAN.
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Khan, Aman Ullah. "Parallel computation of fast Fourier transforms." Thesis, Cardiff University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340239.
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Al-Harbi, Hamad F. "Crystal plasticity finite element simulations using discrete Fourier transforms." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/51788.
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Crystallographic texture and its evolution are known to be major sources of anisotropy in polycrystalline metals. Highly simplified phenomenological models cannot usually provide reliable predictions of the materials anisotropy under complex deformation paths, and lack the fidelity needed to optimize the microstructure and mechanical properties during the production process. On the other hand, physics-based models such as crystal plasticity theories have demonstrated remarkable success in predicting the anisotropic mechanical response in polycrystalline metals and the evolution of underlying texture in finite plastic deformation. However, the integration of crystal plasticity models with finite element (FE) simulations tools (called CPFEM) is extremely computationally expensive, and has not been adopted broadly by the advanced materials development community. The current dissertation has mainly focused on addressing the challenges associated with integrating the recently developed spectral database approach with a commercial FE tool to permit computationally efficient simulations of heterogeneous deformations using crystal plasticity theories. More specifically, the spectral database approach to crystal plasticity solutions was successfully integrated with the implicit version of the FE package ABAQUS through a user materials subroutine, UMAT, to conduct more efficient CPFEM simulations on both fcc and bcc polycrystalline materials. It is observed that implementing the crystal plasticity spectral database in a FE code produced excellent predictions similar to the classical CPFEM, but at a significantly faster computational speed. Furthermore, an important application of the CPFEM for the extraction of crystal level plasticity parameters in multiphase materials has been demonstrated in this dissertation. More specifically, CPFEM along with a recently developed data analysis approach for spherical nanoindentation and Orientation Imaging Microscopy (OIM) have been used to extract the critical resolved shear stress of the ferrite phase in dual phase steels. This new methodology offers a novel efficient tool for the extraction of crystal level hardening parameters in any single or multiphase materials.
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Arof, H. "Texture classification and segmentation using one dimensional discrete Fourier transforms." Thesis, Swansea University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.635797.
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This thesis introduces a texture descriptor that is invariant to rotation. The new texture descriptor utilizes the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of input elements. Since rotating an image by an arbitrary angle does not change pixel intensities in an image but shifts them in circular motion, the notion of producing texture features invariant to rotation using 1-D Fourier transform coefficients can be realized if the relationship between circular motion and spatial shift can be established. By analyzing individual circular neighbourhoods centered at every pixel in an image, local and global texture attributes of the image can be described. Rotating the image has a similar effect as spatially shifting the pixels in the circular neighbourhood around without altering their intensities. A number of sequences can be formed by the intensities of pixels at various fixed distances from the center of the neighbourhood. Fourier transforming the sequences would generate coefficients that contain the texture information of the neighbourhood. From the magnitudes of these coefficients, several rotation invariant features are obtained. The capabilities of the new features are investigated in a number of classification and segmentation experiments. The experimental results compare favourably with those of prominent descriptors like the circular autoregressive model, the wavelet transform, the Gaussian Markov radom field and the co-occurrence matrix. In the majority of the instances, the new method shows superior performance.
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Barrera, David. "Quenched Asymptotics for the Discrete Fourier Transforms of a Stationary Process." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1460652609.
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Sayyah, Jahromi Mohammad Reza Information Technology & Electrical Engineering Australian Defence Force Academy UNSW. "Efficient broadband antenna array processing using the discrete fourier form transform." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Information Technology and Electrical Engineering, 2005. http://handle.unsw.edu.au/1959.4/38690.
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Processing of broadband signals induced on an antenna array using a tapped delay line filter and a set of steering delays has two problems. Firstly one needs to manipulate large matrices to estimate the filter coefficients. Secondly the use of steering delays is not only cumbersome but implementation errors cause loss of system performance. This thesis looks at both of these problems and presents elegant solutions by developing and studying a design method referred to as the DFT method, which does not require steering delays and is computationally less demanding compared to existing methods. Specifically the thesis studies and compares the performance of a time domain element space beamformer using the proposed method and that using an existing method, and develops the DFT method when the processor is implemented in partitioned form. The study presented in the thesis shows that the processors using the DFT method are robust to look direction errors and require less computation than that using the existing method for comparable performance. The thesis further introduces a broadband beamformer design which does not require any steering delays between the sensors and the tapped delay line section as is presently the case. It has the capability of steering the array in an arbitrary direction with a specified frequency response in the look direction while canceling unwanted uncorrelated interferences. The thesis presents and compares the performance of a number of techniques to synthesize an antenna pattern of a broadband array. These techniques are designed to produce isolated point nulls as well as broad sector nulls and to eliminate the need for the steering delays. Two of the pattern synthesis techniques presented in the thesis allow optimization against unwanted interferences in unknown directions. The techniques allow formulation of a beamforming problem such that the processor is not only able to place nulls in specified directions but also able to cancel directional interferences in unknown directions along with a specified frequency response in the look direction over a band of interest. The thesis also presents a set of directional constraints such that one does not need steering delays and an array can be constrained in an arbitrary direction with a specified frequency response. The constraints presented in the thesis are simple to implement. Based on these constraints a pattern synthesis technique for broadband antenna array is also presented.
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Ganesh, Murthy C. N. S. "A Study On Bandpassed Speech From The Point Of Intelligibility." Thesis, Indian Institute of Science, 1989. http://hdl.handle.net/2005/93.
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Speech has been the subject of interest for a very long time. Even with so much advancement in the processing techniques and in the understanding of the source of speech, it is, even today, rather difficult to generate speech in the laboratory in all its aspects. A simple aspect like how the speech can retain its intelligibility even if it is distorted or band passed is not really understood. This thesis deals
with one small feature of speech viz., the intelligibility of speech is retained even when it is bandpassed with a minimum bandwidth of around 1 KHz located any where on the speech
spectrum of 0-4 KHz.
Several experiments have been conducted by the earlier workers by passing speech through various distortors like differentiators, integrators and infinite peak clippers and it is found that the intelligibility is retained to a very large extent in the distorted speech. The integrator and the differentiator remove essentially a certain portion of the spectrum. Therefore, it is thought that the intelligibility of the speech is spread over the entire speech spectrum and that, the intelligibility of speech may not be impaired even when it is bandpassed with a minimum bandwidth and the band may be located any where in the speech spectrum. To test this idea and establish this feature if it exists, preliminary
experiments have been conducted by passing the speech through different filters and it is found that the conjecture seems to be on the right line.
To carry out systematic experiments on this an
experimental set up has been designed and fabricated which consists of a microprocessor controlled speech recording, storing and speech playback system. Also, a personal computer
is coupled to the microprocessor system to enable the storage and processing of the data. Thirty persons drawn from different walks of life like teachers, mechanics and students have been involved for collecting the samples and for
recognition of the information of the processed speech. Even though the sentences like 'This is devices lab' are used to ascertain the effect of bandwidth on the intelligibility, for the purpose of analysis, vowels are used as the speech samples.
The experiments essentially consist of recording words and sentences spoken by the 30 participants and these recorded speech samples are passed through different filters with different bandwidths and central frequencies. The filtered output is played back to the various listeners and
observations regarding the intelligibility of the speech are noted. The listeners do not have any prior information about the content of the speech. It has been found that in almost
all (95%) cases, the messages or words are intelligible for most of the listeners when the band width of the filter is about 1 KHz and this is independent of the location of the pass band in the spectrum of 0-4 KHz. To understand how this feature of speech arises, spectrums of vowels spoken by 30 people have using FFT algorithms on the digitized samples of the speech.
It is felt that there is a cyclic behavior of the spectrum in all the samples. To make sure that the periodicity is present and also to arrive at the periodicity, a moving average procedure is employed to smoothen the spectrum. The smoothened spectrums of all the vowels indeed show a periodicity of about 1 KHz. When the periodicities are analysed the average value of the periodicities has been found to be 1038 Hz with a standard deviation of 19 Hz. In view of this it is thought that the acoustic source
responsible for speech must have generated this periodic spectrum, which might have been modified periodically to imprint the intelligibility. If this is true, one can perhaps easily understand this feature of the speech viz., the intelligibility is retained in a bandpassed speech of bandwidth 1 K H z . the pass band located any where in the speech spectrum of 0-4 KHz. This thesis describing the experiments and the analysis of the speech has been presented in 5 chapters. Chapter 1 deals with the basics of speech and the processing tools used to analyse the speech signal. Chapter 2 presents the literature survey from where the present problem is tracked down. Chapter 3 describes the details of the structure and the fabrication of the experimental setup that has been used. In chapter 4, the detailed account of the way in which the
experiments are conducted and the way in which the speech is analysed is given. In conclusion in chapter 5, the work is summarised and the future work needed to establish the mechanism of speech responsible for the feature of speech described in this thesis is suggested.
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Bleiler, Sarah K. "Orthogonal filters and the implications of wrapping on discrete wavelet transforms." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002676.
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Lo, King Chuen. "Theory and realization of novel algorithms for random sampling in digital signal processing." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5239/.
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Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N(^2). The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N"^. The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% , of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement instruments where computing a spectrum is either minimal or not required. Such applications in instrumentation are easily found in the literature. In this thesis, two applications in digital signal processing are introduced. (5) To suggest an inverse transformation for random sampling so as to complete a two-way process and to broaden its scope of application. Apart from the above, a case study of realizing in a transputer network the prime factor algorithm with regular sampling is given in Chapter 2 and a rough estimation of the signal-to-noise ratio for a spectrum obtained from random sampling is found in Chapter 3. Although random sampling is alias-free, problems in computational complexity and noise prevent it from being adopted widely in engineering applications. In the conclusions, the criteria for adopting random sampling are put forward and the directions for its development are discussed.
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Hickman, Jonathan Edward. "Topics in affine and discrete harmonic analysis." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10559.
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In this thesis a number of problems in harmonic analysis of a geometric flavour are discussed and, in particular, the Lebesgue space mapping properties of certain averaging and Fourier restriction operators are studied. The first three chapters focus on the perspective afforded by affine-geometrical considerations whilst the remaining chapter considers some discrete variants of these problems. In Chapter 1 there is an overview of the basic affine theory of the aforementioned operators and, in particular, the affine arc-length and surface measures are introduced. Chapter 2 presents work of the author, submitted for publication, concerning an operator which takes averages of functions on Euclidean space over both translates and dilates of a fixed polynomial curve. Moreover, the averages are taken with respect to the affine arc-length; this allows one to prove Lebesgue space estimates with a substantial degree of uniformity in the constants. The sharp range of uniform estimates is obtained in all dimensions except for an endpoint. Chapter 3 presents some work of the author, published in Mathematika, concerning a family of Fourier restriction operators closely related to the averaging operators discussed in Chapter 2. Specifically, a Fourier restriction estimate is obtained for a broad class of conic surfaces by introducing a certain measure which exhibits a special kind of affine invariance. Again, the sharp range of estimates is obtained, but the results are limited to the case of 2-dimensional cones. Finally, Chapter 4 discusses some recent joint work of the author and Jim Wright considering the restriction problem over rings of integers modulo a prime power. The sharp range of estimates is obtained for Fourier restriction to the moment curve in finitely-generated free modules over such rings. This is achieved by lifting the problem to the p-adics and applying a classical argument of Drury in this setting. This work aims to demonstrate that rings of integers offer a simplified model for the Euclidean restriction problem.
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Miar, Yasin. "Improved Wideband Spectrum Sensing Methods for Cognitive Radio." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23333.
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Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.
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baktir, selcuk. "Frequency Domain Finite Field Arithmetic for Elliptic Curve Cryptography." Digital WPI, 2008. https://digitalcommons.wpi.edu/etd-dissertations/272.
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Efficient implementation of the number theoretic transform(NTT), also known as the discrete Fourier transform(DFT) over a finite field, has been studied actively for decades and found many applications in digital signal processing. In 1971 Schonhage and Strassen proposed an NTT based asymptotically fast multiplication method with the asymptotic complexity O(m log m log log m) for multiplication of $m$-bit integers or (m-1)st degree polynomials. Schonhage and Strassen's algorithm was known to be the asymptotically fastest multiplication algorithm until Furer improved upon it in 2007. However, unfortunately, both algorithms bear significant overhead due to the conversions between the time and frequency domains which makes them impractical for small operands, e.g. less than 1000 bits in length as used in many applications. With this work we investigate for the first time the practical application of the NTT, which found applications in digital signal processing, to finite field multiplication with an emphasis on elliptic curve cryptography(ECC). We present efficient parameters for practical application of NTT based finite field multiplication to ECC which requires key and operand sizes as short as 160 bits in length. With this work, for the first time, the use of NTT based finite field arithmetic is proposed for ECC and shown to be efficient. We introduce an efficient algorithm, named DFT modular multiplication, for computing Montgomery products of polynomials in the frequency domain which facilitates efficient multiplication in GF(p^m). Our algorithm performs the entire modular multiplication, including modular reduction, in the frequency domain, and thus eliminates costly back and forth conversions between the frequency and time domains. We show that, especially in computationally constrained platforms, multiplication of finite field elements may be achieved more efficiently in the frequency domain than in the time domain for operand sizes relevant to ECC. This work presents the first hardware implementation of a frequency domain multiplier suitable for ECC and the first hardware implementation of ECC in the frequency domain. We introduce a novel area/time efficient ECC processor architecture which performs all finite field arithmetic operations in the frequency domain utilizing DFT modular multiplication over a class of Optimal Extension Fields(OEF). The proposed architecture achieves extension field modular multiplication in the frequency domain with only a linear number of base field GF(p) multiplications in addition to a quadratic number of simpler operations such as addition and bitwise rotation. With its low area and high speed, the proposed architecture is well suited for ECC in small device environments such as smart cards and wireless sensor networks nodes. Finally, we propose an adaptation of the Itoh-Tsujii algorithm to the frequency domain which can achieve efficient inversion in a class of OEFs relevant to ECC. This is the first time a frequency domain finite field inversion algorithm is proposed for ECC and we believe our algorithm will be well suited for efficient constrained hardware implementations of ECC in affine coordinates.
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Martins, Carlos Henrique Nascimento. "Estudo e implementação de um analisador de harmônicos variantes no tempo." Universidade Federal de Juiz de Fora (UFJF), 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/4176.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Esta tese apresenta as etapas de desenvolvimento de um sistema de monitoramento de parâmentos de qualidade de energia dedicado a análise de harmônicos variantes no tempo através do equipamento denominado AHVT (Analisador de Harmônicos Variantes no Tempo). O desenvolvimento do trabalho é composto por: (i) estudo e implementação MATLAB de algoritmos para processamento em tempo real, com capacidade de sintonização dos componentes harmônicos; (ii) análise e desenvolvimento de estratégias para detecção e validação da presença de interharmônicos próximos à frequência fundamental e suas consequência na estimação de parâmetros como fase, amplitude e frequência para o componente fundamental, (iii) proposta de implementação do dispositivo, sistema de aquisição/ condicionamento de sinais/ filtragem, sistema de conversão analógico digital e plataforma de processamentoDSP/FPGA, sistema de transmissão de dados e plataformas de análise online/offline dos eventos de harmônicos variantes no tempo; (iv) plataforma de simulação do Analisador de Harmônicos Variantes no Tempo (AHVT) para estudo dos métodos de trigger para detecção e captura dos eventos.
In this work is presented the steps of development and implementation of a Power Quality paramaters monitoring system with main goal events denomined ”time arying harmonics”named of Time Varying Harmonic Analyzer. The development is comprises:(i) research and implementation of real time algorithms with capable to tuning harmonic waves,(ii) Analyze and research/development of strategies for detect and validation of interharmonics with frequencies near of fundamental, and conseguencies and challenges to phase, magnitude and frequency estimation with presence interharmonic waveform (iii) The proposal of a hardware design including analog to digital conversion and digital signal processing plataform, broadcast data link and IHM(Interface Human Machine) for online and offline analyzes to time varying harmonic analyzer;(iiii)off-line simulation plataform of Analisador de Harmônicos Variantes no Tempo Time Varying Harmonic Analyzer (TVHA) to trigger detect methods to detection and capture of waveforms.
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Barnhart, Samuel. "Design and Development of a Coherent Detection Rayleigh Doppler Lidar System for Use as an Alternative Velocimetry Technique in Wind Tunnels." University of Dayton / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1595276402371536.
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Madishetty, Suresh. "Design of Multi-Beam Hybrid Digital Beamforming Receivers." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1545178805415923.
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Sarathy, Vivek. "High Spurious-Free Dynamic Range Digital Wideband Receiver for Multiple Signal Detection and Tracking." Wright State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=wright1197910677.
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Lingenbrink, David Alan Jr. "A New Subgroup Chain for the Finite Affine Group." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/55.
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The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
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Logette, Patrice. "Etude et réalisation d'un processeur acousto-optique numérique de traitement des signaux." Valenciennes, 1997. https://ged.uphf.fr/nuxeo/site/esupversions/bbfd31df-2499-46a6-843d-52f346b1db41.
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Un système hybride acousto-optique/numérique axe principalement sur le filtrage F. I. R. A été développé au laboratoire dans le cadre d'une thèse antérieure. L'objet du présent travail est, d'une part, d'améliorer le système existant et, d'autre part, de tester les aptitudes du système ainsi modifié à effectuer d'autres types de calcul. Nous commençons par un résumé des travaux relatifs à l'ancien système, afin de bien positionner le problème. Nous exposons ensuite la conception du nouveau système. Une première partie décrit les modifications des circuits électroniques, avec l'utilisation de circuits de logique programmable de marque Altera. Une seconde partie est dédiée à l'aspect commande. On y détaille le programme de pilotage du système, la création et l'utilisation de modules indépendants pour chaque type de calcul, ainsi que les utilitaires associés (simulation, génération d'algorithmes). Nous terminons par une présentation de quelques exemples de calculs (FIR, IIR, DFT, DCT, corrélation) et évaluons les performances de notre système pour chacun de ces types d’opérations. Le bilan est assez satisfaisant dans l'ensemble, bien que l'apport des circuits Altera ne se soit pas révélé à la hauteur de nos espérances. Le filtrage IIR est le moins performant et nécessiterait la recherche d'autres algorithmes. Cependant, pour être réellement opérationnel, il faudrait améliorer la partie acousto-optique, ou à moyen terme, passer au tout numérique. Nous pourrions, alors, disposer d'un système simple et pratique pour simuler, tester ou valider, sur maquette, des algorithmes ou des sous-systèmes développés au laboratoire dans divers domaines du traitement de signal.
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Dvořák, Vojtěch. "Implementace výpočtu FFT v obvodech FPGA a ASIC." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-220087.
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The aim of this thesis is to design the implementation of fast Fourier transform algorithm, which can be used in FPGA or ASIC circuits. Implementation will be done in Matlab and then this form of implementation will be used as a reference model for implementation of fast Fourier transform algorithm in VHDL. To verify the correctness ofdesign verification enviroment will be created and verification process wil be done. Program that will generate source code for various parameters of the module performing a fast Fourier transform will be created in the last part of this thesis.
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Rodesten, Stephan. "Program för frekvensanalys." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-58157.
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Denna rapport täcker arbetsprocessen bakom att skapa en spektrumanalysator. Läsaren kommer att få läsa om den valda metoden men även alternativa metoder. Utöver detta kommer även de teoretiska delarna bakom varje moment att undersökas samt jämföras med potentiella alternativa lösningar. Projektet har utförts på uppdrag av KA Automation. Syftet med projektet var att skapa en basplattform för analys av ljudfrekvenser. Målet med detta var att kunna identifiera ljudegenskaper i form av frekvenserna hos exempelvis servomotorer i vattenpumpar. Tanken var att i ett senare utvecklingsskede kunna identifiera om och när nya frekvenser dykt upp i ljudprofilen vilket i sådana fall kan resultera i att motorn är i behov av service. Basplattformen är uppbyggd med hjälp av C# och ljudbehandlingsbiblioteket NAudio. Från resultatet kan slutsatsen dras att detta program kan analysera ljud och visa de olika frekvensernas styrka och därmed är en lämplig basplattform för vidareutveckling.This report will cover the work process behind creating a spectrum analyzer. The reader will be able to read about the chosen method but also the alternative methods. Apart from this the theoretical parts behind every moment will also be covered and compared to potential alternative solutions. The project has been carried out on behalf of KA Automation. The purpose of the project was to create a base for analyzing sound frequencies. The goal was to be able to identify sound properties in the form of frequencies in servo motors in for example water pumps. The idea was to be able to in a later development stage be able to identify when new frequencies have entered the audio profile which might result in the motor to be in need of service. The base is created with the help of C# and the sound library NAudio. From the result one can conclude that this program can analyze sound and display the magnitude of its frequency components and is therefore a suitable base for future development.
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Chung, Ming-Shen, and 鐘明聲. "FPGA Implementation of the Discrete Fourier Transform (DFT) and the Discrete Cosine Transform (DCT)." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/01456280849939764692.
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碩士國立高雄第一科技大學
電腦與通訊工程所
90
The Discrete Fourier Transform（DFT）has been widely applied in communcation, speech processing, image processing, radar and sonar systems, etc. The architecture of DFT implement can be classified into two fields：（1）one is a pipelined systolic architecture,（2）the other is a memory-based architecture. Discrete Cosine Transform（DCT）has been commonly adopted in the various atandardsfor image compression while FPGA has become a new trend of ASIC design, so we will apply FPGA techinque to implement the DFT and the DCT. This thesis deals with how to use FPGA techinque to implement： （1）the pipelined systolic array architecture that requires log2N complex multipliers, 2log2N complex adders, 2log2N multiplexers, N delay elements and is able to provide a throughput of one transform sample per clock cycle; （2）the memory-based architecture that consists of three two-port RAM’s, one ROM, one complex multiplier, two complex adders, one multiplexer, and has capability of computing one transform sample every log2N+1 clock cycles on average; （3）Improved architecture in（2）under increasing little hardware that spends half of run time, i.e.N(log2N)/2; （4）2D-DFT that use architecture in（2）of 1D-DFT; （5）DCT operation and 2D-DCT operation.
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Tsai, Fong-Mao, and 蔡豐懋. "Image watermarking based on discrete fractional Fourier transforms." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/08912139702596715078.
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碩士中原大學
通訊工程碩士學位學程
102
In this thesis, to find robust watermarking schemes, we use discrete fractional Fourier transform (DFRFT) and its other four generalized transforms to embed watermarks. They are methods of embedding watermarks in transform domains. In [1], discrete Fractional random transform (DFRNT) was used to embed watermarks. We extend that method and use five transforms to replace DFRNT for watermark embedding and extracting. Then, we attack the watermarked images. The attacks include cropping, salt-and-pepper noise and Gaussian low pass filter. After attacks, we extract the watermark to observe the limits of these transforms to resist attacks and to analyze the robustness. The resistances of DFRFT and multiple-parameter discrete fractional Fourier transform (MPDFRFT) against cropping are the worst. The random discrete fractional Fourier transform (Random DFRFT) has the best performance against cropping and salt-and-pepper noise attack. Real discrete fractional Fourier transform (Real DFRFT) and real discrete fractional Hartley transform (Real DFRHT) have good performance against cropping. All the five transforms can withstand the attack of Gaussian low pass filter. Random DFRFT has the best robustness in this thesis, because it has a higher randomness. Random DFRFT is suitable for watermark applications. Furthermore, there are two real transforms (Real DFRFT, Real DFRHT). The eigenvectors of both transforms are random, and all the values in the transformation process are real, they are suitable for resist cropping attack.
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WU, JIA-LIN, and 吳家麟. "Fast algorithms and architectures for discrete fourier transforms and digital convolutions." Thesis, 1986. http://ndltd.ncl.edu.tw/handle/37367192987084224568.
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Hsu, Fang-Chii, and 許芳綺. "Efficient Memory Arrangement Methods and VLSI Implementations for Discrete Fourier and Cosine Transforms." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/61599713560978766382.
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碩士國立中山大學
資訊工程學系研究所
89
The thesis proposes using the efficient memory arrangement methods for the implementation of radix-r multi-dimensional Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT). By using the memory instead of the registers to buffer and reorder data, hardware complexity is significantly reduced. We use the recursive architecture that requires only one arithmetic-processing element to compute the entire DFT/DCT operation. The algorithm is based on efficient coefficient matrix factorization and data allocation. By exploiting the features of Kronecker product representation in the fast algorithm, the multi-dimensional DFT/DCT operation is converted into its corresponding 1-D problem and the intermediate data is stored in several memory units. In addition to the smaller area, we also propose a method to reduce the power consumption of the DFT/DCT processors.
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Bittens, Sina Vanessa. "Sparse Fast Trigonometric Transforms." Doctoral thesis, 2019. http://hdl.handle.net/21.11130/00-1735-0000-0003-C16D-9.
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Zaeim, Ramin. "Direction of arrival estimation technique for narrow-band signals based on spatial Discrete Fourier Transform." Thesis, 2018. https://dspace.library.uvic.ca//handle/1828/9948.
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This work deals with the further development of a method for Direction of Arrival (DOA) estimation based on the Discrete Fourier Transform (DFT) of the sensor array output. In the existing DFT-based algorithm, relatively high SNR is considered, and it is assumed that a large number of sensors are available.
In this study an overview of some of the most commonly used DOA estimation techniques will be presented. Then the performance of the DFT method will be analyzed and compared with the performance of existing techniques. Two main objectives will be studied, firstly the reduction of the number of sensors and secondly the performance of the DFT based technique in the presence of noise.
Experimental simulations will be presented to illustrate that in absence of noise, the proposed method is very fast and using just one snapshot is sufficient to accurately estimate DOAs. Also, in presence of noise, the method is still relatively fast and using a small number of snapshots, it can accurately estimate DOAs.
The above mentioned properties are the result of taking an average of the peaks of the DFTs, X_n (k), obtained from a sequence of N_s snapshots. With N_s sufficiently large, the average over N_s snapshots approaches expected value. Also, the conditions that should be satisfied to avoid overlapping of main-lobes, and thus loosing the DOA of some signals, in the DFT spectrum are examined.
This study further analyzes the performance of the proposed method as well as two other commonly used algorithms, MUSIC and conventional beamformer. An extensive simulation was conducted and different features of the spatial DFT technique, such as accuracy, resolution, sensitivity to noise, effect of multiple snapshots and the number of sensors were evaluated and compared with those of existing techniques. The simulations indicate that in most aspects the proposed spatial DFT algorithm outperforms the other techniques.Graduate
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Chiu, Wei-Ting, and 邱偉庭. "Digital Image Security Applications Based on Discrete Fractional Fourier Transforms and Random Phase Encoding." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/ps58d5.
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碩士中原大學
通訊工程碩士學位學程
103
In this study, we propose an image watermarking algorithm based on discrete fractional Fourier transform (DFRFT) and its extended transforms with random phase encoding (RPE) base on Guo’s method [1]. We also use discrete fractional Fourier transform and its extended transforms with random phase encoding to encrypt double images using Tao’s technology [2].We use multiple-parameter discrete Fourier fractional (MPDFRFT), random discrete fractional Fourier transform (RDFRFT), and real discrete fractional Fourier transform (Real-DFRFT) to replace discrete fractional Fourier transform for embedding digital watermark and encrypting double images. Then we attack the watermarked image and encrypted images to discuss the robustness of these two methods. The DFRFT has the best robustness in the random phase encoding of digital watermarking. The RDFRFT has the best robustness in the random phase encoding for encrypting double images. The RDFRFT and the Real-DFRFT can be applied to increases image security, because of their large number of free parameters.
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Tai, Yu, and 戴譽. "Applications of Multiple-Parameter Discrete Fractional Fourier Transforms on Digital Image Encryption and Watermarking." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/y84tq2.
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碩士中原大學
電機工程研究所
106
Multiple-parameter discrete fractional Fourier transforms have many free parameters and these parameters can be used as encryption keys that make cryptosystems become more secure. In this thesis, several multiple-parameter discrete fractional Fourier transforms are applied in digital image encryption and watermarking. There are two main topics of digital image encryption including asymmetric double random phase encoding and multiple-image encryption with asymmetric cryptosystem. Asymmetric double random phase encoding is the improved version of double random phase encoding which is based on a phase-truncation in Fourier domain that creates a new key during encoding. This cryptosystem has the feature of the different encoding and decoding keys. This asymmetric characteristic makes the cryptosystem secure against the known-plaintext attack and the output of the encrypted image is a real stationary white noise image. The next topic is about the multiple-image encryption with asymmetric cryptosystem. It is based on phase-truncation and amplitude-truncation that make the cryptosystem’s keys asymmetric and can also encrypt multiple images in one time. And the operation of combined-phase makes the random phase keys in encryption must be used during decryption, which improves its security. The employed transform of the two cryptosystems mentioned above is the Fourier transform. This thesis will change that transform to multiple-parameter discrete fractional Fourier transforms that can increase the complexity of keys but also without sacrificing the sensitivity of phase keys and amplitude keys. As to the digital image watermarking, image watermarking based on fractional Fourier transform and random phase encoding is a method that hides the watermark into the phase. There is a drawback that the watermark still can be retrieved when the host image is fully cropped. To avoid this problem, this thesis tries to embed the watermark into the amplitude domain and employ the multiple-parameter discrete fractional Fourier transforms. But this thesis discovers a safety issue that the illegal user can still extract the watermark even without the amplitude key. The last topic is the hierarchical double random phase encrypted image watermarking using multiple parameters fractional Fourier transforms. The most important feature of the method is to divide the watermark into several pieces and send those segments to different owners. Only the highest class user owns all of the keys for retrieving the correct watermark. The thesis proposes to change the employed transform to multiple-parameter discrete fractional Fourier transforms that not just increase the number of free parameters and higher error sensitivity but also maintain the robustness against image attacks like cropping attack and salt and pepper noise attack.
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Suresh, K. "MDCT Domain Enhancements For Audio Processing." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/1184.
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Modified discrete cosine transform (MDCT) derived from DCT IV has emerged as the most suitable choice for transform domain audio coding applications due to its time domain alias cancellation property and de-correlation capability. In the present research work, we focus on MDCT domain analysis of audio signals for compression and other applications. We have derived algorithms for linear filtering in DCT IV and DST IV domains for symmetric and non-symmetric filter impulse responses. These results are also extended to MDCT and MDST domains which have the special property of time domain alias cancellation. We also derive filtering algorithms for the DCT II and DCT III domains. Comparison with other methods in the literature shows that, the new algorithm developed is computationally MAC efficient. These results are useful for MDCT domain audio processing such as reverb synthesis, without having to reconstruct the time domain signal and then perform the necessary filtering operations.
In audio coding, the psychoacoustic model plays a crucial role and is used to estimate the masking thresholds for adaptive bit-allocation. Transparent quality audio coding is possible if the quantization noise is kept below the masking threshold for each frame. In the existing methods, the masking threshold is calculated using the DFT of the signal frame separately for MDCT domain adaptive quantization. We have extended the spectral integration based psychoacoustic model proposed for sinusoidal modeling of audio signals to the MDCT domain. This has been possible because of the detailed analysis of the relation between DFT and MDCT; we interpret the MDCT coefficients as co-sinusoids and then apply the sinusoidal masking model. The validity of the masking threshold so derived is verified through listening tests as well as objective measures.
Parametric coding techniques are used for low bit rate encoding of multi-channel audio such as 5.1 format surround audio. In these techniques, the surround channels are synthesized at the receiver using the analysis parameters of the parametric model. We develop algorithms for MDCT domain analysis and synthesis of reverberation. Integrating these ideas, a parametric audio coder is developed in the MDCT domain. For the parameter estimation, we use a novel analysis by synthesis scheme in the MDCT domain which results in better modeling of the spatial audio. The resulting parametric stereo coder is able to synthesize acceptable quality stereo audio from the mono audio channel and a side information of approximately 11 kbps. Further, an experimental audio coder is developed in the MDCT domain incorporating the new psychoacoustic model and the parametric model.
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Anoh, Kelvin O. O., N. T. Ali, Hassan S. O. Migdadi, Raed A. Abd-Alhameed, Tahereh S. Ghazaany, Steven M. R. Jones, James M. Noras, and Peter S. Excell. "Performance comparison of MIMO-DWT and MIMO-FrFT multicarrier systems." 2013. http://hdl.handle.net/10454/9607.
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NoIn this work, we discuss two new multicarrier modulating kernels that can be adopted for multicarrier signaling. These multicarrier transforms are the fractional Forurier transform (FrFT) and discrete wavelet transforms (DWT). At first, we relate the transforms in terms of mathematical relationships, and then using numerical and simulation comparisons we show their performances in terms of bit error ratio (BER) for Multiple Input Multiple Output (MIMO) applications. Numerical results using BPSK and QPSK support that both can be applied for multicarrier signaling, however, it can be resource effective to drive the DWT as the baseband multicarrier kernel at the expense of the FrFT
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Hulett, David Alexander. "De Fourier a wavelets : un breve recorrido por el análisis tiempo-frecuencia." Bachelor's thesis, 2020. http://hdl.handle.net/11086/15941.
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Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.Un pequeño tour por el análisis de Fourier. Definimos a la transformada continua de Fourier, presentamos y estudiamos los resultados principales de la serie de Fourier y de la transformada de Fourier discreta. Analizamos cómo hacer la transición de serie a transformada continua y de transformada discreta a la serie. Para estudiar la estructura tiempo-frecuencia de una función presentamos a las transformadas atómicas y estudiamos dos ejemplos: la STFT y la transformada wavelet.
A small tour of Fourier analysis. We define the continuous Fourier transform, and we present and study the main results regarding the Fourier series and the discrete Fourier transform. We analyse how to transition from the series to the continuous transform and from the discrete transform to the series. In order to study the time-frequency structure of a function we introduce the atomic transforms and we focus our attention on two examples: the STFT and the wavelet transform.
Fil: Hulett, David Alexander. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.