Relevant bibliographies by topics / Discrete Fourier transforms (DFTs)

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  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Discrete Fourier transforms (DFTs)'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Discrete Fourier transforms (DFTs)"

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Mahmood, Faisal, Märt Toots, Lars-Göran Öfverstedt, and Ulf Skoglund. "Algorithm and Architecture Optimization for 2D Discrete Fourier Transforms with Simultaneous Edge Artifact Removal." International Journal of Reconfigurable Computing 2018 (August 6, 2018): 1–17. http://dx.doi.org/10.1155/2018/1403181.

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Two-dimensional discrete Fourier transform (DFT) is an extensively used and computationally intensive algorithm, with a plethora of applications. 2D images are, in general, nonperiodic but are assumed to be periodic while calculating their DFTs. This leads to cross-shaped artifacts in the frequency domain due to spectral leakage. These artifacts can have critical consequences if the DFTs are being used for further processing, specifically for biomedical applications. In this paper we present a novel FPGA-based solution to calculate 2D DFTs with simultaneous edge artifact removal for high-performance applications. Standard approaches for removing these artifacts, using apodization functions or mirroring, either involve removing critical frequencies or necessitate a surge in computation by significantly increasing the image size. We use a periodic plus smooth decomposition-based approach that was optimized to reduce DRAM access and to decrease 1D FFT invocations. 2D FFTs on FPGAs also suffer from the so-called “intermediate storage” or “memory wall” problem, which is due to limited on-chip memory, increasingly large image sizes, and strided column-wise external memory access. We propose a “tile-hopping” memory mapping scheme that significantly improves the bandwidth of the external memory for column-wise reads and can reduce the energy consumption up to 53%. We tested our proposed optimizations on a PXIe-based Xilinx Kintex 7 FPGA system communicating with a host PC, which gives us the advantage of further expanding the design for biomedical applications such as electron microscopy and tomography. We demonstrate that our proposed optimizations can lead to 2.8× reduced FPGA and DRAM energy consumption when calculating high-throughput 4096×4096 2D FFTs with simultaneous edge artifact removal. We also used our high-performance 2D FFT implementation to accelerate filtered back-projection for reconstructing tomographic data.
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He, Y., K. Hueske, J. Götze, and E. Coersmeier. "Matrix-Vector Based Fast Fourier Transformations on SDR Architectures." Advances in Radio Science 6 (May 26, 2008): 89–94. http://dx.doi.org/10.5194/ars-6-89-2008.

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Abstract. Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
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Yang, Y., M. Crimp, R. A. Tomlinson, and E. A. Patterson. "Quantitative measurement of plastic strain field at a fatigue crack tip." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2144 (March 14, 2012): 2399–415. http://dx.doi.org/10.1098/rspa.2011.0682.

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A novel approach is introduced to map the mesoscale plastic strain distribution resulting from heterogeneous plastic deformation in complex loading and component geometries, by applying the discrete Fourier transform (DFT) to backscattered electron (BSE) images of polycrystalline patches. These DFTs are then calibrated against the full width at half the maximum of the central peak of the DFTs collected from the same material tested under in situ scanning electron microscopy uniaxial tensile conditions, which indicates a close relationship with the global tensile strain. In this work, the technique is demonstrated by measuring the residual strain distribution and plastic zone size around a fatigue crack tip in a commercially pure titanium compact tension specimen, by collecting BSE images in a 15×15 array of 115 μm square images around the fatigue crack tip. The measurement results show good agreement with the plastic zone size and shape measured using thermoelastic stress analysis.
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Peng, Yaqiu, and Mingqi Li. "Discrete Fourier Transform-Based Block Faster-Than- Nyquist Transmission for 5G Wireless Communications." Applied Sciences 10, no. 4 (February 14, 2020): 1313. http://dx.doi.org/10.3390/app10041313.

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Faster-than-Nyquist (FTN) signaling is regarded as a potential candidate for improving data rate and spectral efficiency of 5G new radio (NR). However, complex detectors have to be utilized to eliminate the inter symbol interference (ISI) introduced by time-domain packing and the inter carrier interference (ICI) introduced by frequency-domain packing. Thus, the exploration of low complexity transceiver schemes and detectors is of great importance. In this paper, we consider a discrete Fourier transform (DFT) block transmission for multi-carrier FTN signaling, i.e., DBT-MC-FTN. With the aid of DFTs/IDFTs and frequency domain windowing, time- and frequency domain packing can be implemented flexibly and efficiently. At the receiver, the inherent ISI and ICI can be canceled via a soft successive interference cancellation (SIC) detector. The effectiveness of the detector is verified by the simulation over the additive white Gaussian noise channel and the fading channel. Furthermore, based on the characteristics of the efficient architecture of DFT-MC-FTN, two pilot-aided channel estimation schemes, i.e., time-division-multiplexing DBT-MC-FTN symbol-level pilot, and frequency-division-multiplexing subcarrier-level pilot within the DBT-MC-FTN symbol, respectively, are also derived. Numerical results show that the proposed channel estimation schemes can achieve high channel estimation accuracy.
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SAKK, ERIC. "ON THE COMPUTATION OF MOLECULAR SURFACE CORRELATIONS FOR PROTEIN DOCKING USING FOURIER TECHNIQUES." Journal of Bioinformatics and Computational Biology 05, no. 04 (August 2007): 915–35. http://dx.doi.org/10.1142/s0219720007002916.

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The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.
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de Oliveira Neto, Jose R., and Juliano B. Lima. "Discrete Fractional Fourier Transforms Based on Closed-Form Hermite–Gaussian-Like DFT Eigenvectors." IEEE Transactions on Signal Processing 65, no. 23 (December 1, 2017): 6171–84. http://dx.doi.org/10.1109/tsp.2017.2750105.

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Han, Feng, Yao Lin Liu, Zhen Liu, and Hai Dong Zeng. "Comments on Errors of DFT Spectrum." Applied Mechanics and Materials 568-570 (June 2014): 189–92. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.189.

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Discrete Fourier transform (DFT/FFT) spectrums contain a variety of inherent errors in asynchronous sampling. Spectrum analysis with the accuracy above 10-3 are generally challenging issues. This work divides the DFT procedure into four signal transforms and exams six spectrum errors originated from these distortions. Besides the review of traditional errors, a so-called energy loss-gain (ELG) error is briefly introduced, which is proved to be a considerable error on the basis of Parseval's theorem. With the help of full error analysis mentioned here and the further development of analytical error estimators, it is expectable to obtain a DFT spectrum with a specified accuracy.
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BI, GUOAN, A. C. KOT, and ZIHOU MENG. "GENERALISED SPLIT-RADIX ALGORITHMS FOR DFT." Journal of Circuits, Systems and Computers 08, no. 03 (June 1998): 405–9. http://dx.doi.org/10.1142/s0218126698000201.

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This letter presents a general split-radix algorithm based on the decimation-in-time decomposition. It can flexibly compute the discrete Fourier transforms of length-q*2m where q is an odd integer. In comparison with other reported algorithms, our proposed one supports a wider range of sequence lengths, achieves a reduction of arithmetic operations and requires a simple computational structure.
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Wang, Bangbing, Bo Sun, Jiaxin Wang, Jamin Greenbaum, Jingxue Guo, Laura Lindzey, Xiangbin Cui, Duncan A. Young, Donald D. Blankenship, and Martin J. Siegert. "Removal of ‘strip noise’ in radio-echo sounding data using combined wavelet and 2-D DFT filtering." Annals of Glaciology 61, no. 81 (March 28, 2019): 124–34. http://dx.doi.org/10.1017/aog.2019.4.

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ABSTRACTRadio-echo sounding (RES) can be used to understand ice-sheet processes, englacial flow structures and bed properties, making it one of the most popular tools in glaciological exploration. However, RES data are often subject to ‘strip noise’, caused by internal instrument noise and interference, and/or external environmental interference, which can hamper measurement and interpretation. For example, strip noise can result in reduced power from the bed, affecting the quality of ice thickness measurements and the characterization of subglacial conditions. Here, we present a method for removing strip noise based on combined wavelet and two-dimensional (2-D) Fourier filtering. First, we implement discrete wavelet decomposition on RES data to obtain multi-scale wavelet components. Then, 2-D discrete Fourier transform (DFT) spectral analysis is performed on components containing the noise. In the Fourier domain, the 2-D DFT spectrum of strip noise keeps its linear features and can be removed with a ‘targeted masking’ operation. Finally, inverse wavelet transforms are performed on all wavelet components, including strip-removed components, to restore the data with enhanced fidelity. Model tests and field-data processing demonstrate the method removes strip noise well and, incidentally, can remove the strong first reflector from the ice surface, thus improving the general quality of radar data.
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Lai, Chao-Yuan, Tien-Yen Yang, and Chih-Wen Liu. "Performance of Implementing Smart DFT in Micro Phasor Measurement Unit." E3S Web of Conferences 69 (2018): 01005. http://dx.doi.org/10.1051/e3sconf/20186901005.

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The advance of the signal processing, this paper implement a more accurate digital measurement algorithm, Smart DFT(SDFT) in Micro Phasor Measurement Unit(μPMU), which is based on Discrete Fourier Transforms(DFT) to estimate frequency information from Taiwan power system. μPMU, the sensor we plan to acquire the information from the power system by using the signal of outlet voltage-level 110V in Taiwan, such as frequency, voltage and angle. The performance of SDFT implemented in μPMU represents a more precise frequency information when frequency fluctuation occurred just as the frequency of power system. We offer the results of simulations, stable frequency generated from waveform generator and real frequency from main electricity to compare SDFT with DFT method which implemented in μPMU.
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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 &amp 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 &amp 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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Books on the topic "Discrete Fourier transforms (DFTs)"

1

Henson, Van Emden. DFTS on irregular grids: The anterpolated DFT. Monterey, Calif: Naval Postgraduate School, 1992.

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Briggs, William L. The DFT: An owner's manual for the discrete Fourier transform. Philadelphia: Society for Industrial and Applied Mathematics, 1995.

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Chu, Eleanor Chin-hwa. Discrete and Continuous Fourier Transforms. London: Taylor and Francis, 2008.

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Chu, Eleanor Chin-hwa. Discrete and continuous fourier transforms analysis. Boca Raton, Fla: Chapman & Hall/CRC Press, 2008.

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Discrete Fourier transforms and their applications. Bristol, England: Adam Hilger, 1986.

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Mathematics of the discrete Fourier transform (DFT): With music and audio applicaitons. [S.l.]: W3K Pub., 2003.

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Chu, Eleanor Chin-hwa. Discrete and continuous fourier transforms: Analysis, applications and fast algorithms. Boca Raton, Fla: CRC Press, 2008.

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Chu, Eleanor Chin-hwa. Discrete and continuous fourier transforms: Analysis, applications and fast algorithms. Boca Raton, Fla: CRC Press, 2008.

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F, Doyle James. Wave propagation in structures: Spectral analysis using fast discrete Fourier transforms. 2nd ed. New York: Springer, 1997.

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F, Doyle James. Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms. New York, NY: Springer New York, 1997.

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Book chapters on the topic "Discrete Fourier transforms (DFTs)"

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Zieliński, Tomasz P. "Discrete Fourier Transforms: DtFT and DFT." In Starting Digital Signal Processing in Telecommunication Engineering, 65–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49256-4_4.

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Firth, Jean M. "Fast Fourier transforms." In Discrete Transforms, 156–77. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2358-7_7.

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Firth, Jean M. "The discrete Fourier transform." In Discrete Transforms, 117–40. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2358-7_5.

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Heideman, Michael T. "Multiplicative Complexity of Discrete Fourier Transform." In Multiplicative Complexity, Convolution, and the DFT, 76–107. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_5.

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Jerri, Abdul J. "Discrete Fourier Transforms." In Linear Difference Equations with Discrete Transform Methods, 281–328. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-5657-9_4.

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Plonka, Gerlind, Daniel Potts, Gabriele Steidl, and Manfred Tasche. "Discrete Fourier Transforms." In Numerical Fourier Analysis, 107–57. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04306-3_3.

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Firth, Jean M. "The Fourier transform. Convolution of analogue signals." In Discrete Transforms, 25–53. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2358-7_2.

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Firth, Jean M. "Fourier series, integral theorem, and transforms: a review." In Discrete Transforms, 1–24. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2358-7_1.

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Firth, Jean M. "Simplification and factorization of the discrete Fourier transform matrix." In Discrete Transforms, 141–55. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2358-7_6.

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Wong, M. W. "Wavelet Transforms and Filter Banks." In Discrete Fourier Analysis, 61–66. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0116-4_10.

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Conference papers on the topic "Discrete Fourier transforms (DFTs)"

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Xu, Y. F., and W. D. Zhu. "Efficient and Accurate Calculation of Discrete Frequency Response Functions and Impulse Response Functions." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47779.

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Modal properties of a structure can be identified by experimental modal analysis (EMA). Discrete frequency response functions (FRFs) and impulse response functions (IRFs) between responses and excitation are bases for EMA. In calculation of a discrete FRF, discrete Fourier transform (DFT) is applied to both response and excitation data series, and a transformed data series in DFT is virtually extended to have an infinite length and be periodic with a period equal to the length of the series; the resulting periodicity can be physically incorrect in some cases, which depends on an excitation technique used. There are various excitation techniques in EMA, and periodic extension in DFT for EMA using periodic random and burst random excitation is physically correct. However, EMA using periodic random excitation needs a relatively long excitation time to have responses to be steady-state and periodic, and EMA using burst random excitation needs a long sampling period for responses to decay to zero, which can result in relatively long response and excitation data series and necessitate a large number of spectral lines for associated DFTs, especially for a high sampling frequency. An efficient and accurate methodology for calculating discrete FRFs and IRFs is proposed here, by which fewer spectral lines are needed and accuracies of resulting FRFs and IRFs can be maintained. The relationship between an IRF from the proposed methodology and that from the least-squares method is shown. A new coherence function that can evaluate qualities of FRFs and IRFs from the proposed methodology in the frequency domain is used, from which meaningful coherence function values can be obtained even with response and excitation series of one sampling period. Based on the new coherence function, a fitting index is used to evaluate overall qualities of the FRFs and IRFs. The proposed methodology was numerically and experimentally applied to a two-degree-of-freedom mass-spring-damper system and an aluminum plate to estimate their FRFs, respectively. In the numerical example, FRFs from the proposed methodology agree well with the theoretical one; in the experimental example, a FRF from the proposed methodology with a random impact series agreed well with the benchmark one from a single impact test.
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Yao, Xueyang, and Natalie Baddour. "Numerical Computation of the Discrete 2D Fourier Transform in Polar Coordinates." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85616.

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The discrete Fourier transform in Cartesian coordinates has proven to be invaluable in many disciplines. However, in application such as photoacoustics and tomography, a discrete 2D-Fourier transform in polar coordinates is needed. In this paper, a discrete 2D-Fourier transform in polar coordinates is presented. It is shown that numerical implementation is best achieved by interpreting the transform as a 1D-discrete Fourier transform (DFT), a 1D-discrete Hankel transform (DHT) and a 1D-discrete inverse transform (IDFT) in sequence. The transform is tested by numerical simulations with respect to accuracy and precision for computation of the continuous 2D transform at specific discrete points. It was found that both the forward and inverse transform showed good accuracy to approximate the continuous Fourier transform. Moreover, good precision results were obtained, which indicate that the proposed transform itself does not add much error.
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Davis, John M., Ian A. Gravagne, and Robert J. Marks. "Time scale discrete Fourier transforms." In 2010 42nd Southeastern Symposium on System Theory (SSST 2010). IEEE, 2010. http://dx.doi.org/10.1109/ssst.2010.5442859.

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Khalil, Ethar H. "EHK Index Method for Calculating Discrete Fourier Transform." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86442.

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A new mathematical model has been achieved, for the calculation of DFT and its inversion depending on the indices which represent the shortest way for referring to the elements, pixels or pixels in each slide dealing with 1-D, 2-D, and 3-D digital signals respectively. This method indicates clearly the contribution factor of each input signal element in each output signal element.
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L. Fontaine, Fred. "Multi Resolution Lattice Discrete Fourier Transform (MRL-DFT)." In 4th International Conference on Information Technology, Control, Chaos, Modeling and Applications. Academy & Industry Research Collaboration Center (AIRCC), 2017. http://dx.doi.org/10.5121/csit.2017.70706.

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Wolf, Kurt Bernardo. "Discrete and finite fractional Fourier transforms." In Frontiers in Optics. Washington, D.C.: OSA, 2003. http://dx.doi.org/10.1364/fio.2003.waa8.

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Mitra, S., and A. Srinivasan. "Small Discrete Fourier Transforms on GPUs." In 2011 11th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid). IEEE, 2011. http://dx.doi.org/10.1109/ccgrid.2011.14.

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Oraintara, Soontorn. "The generalized discrete fractional fourier transforms." In Proceedings of ICASSP '02. IEEE, 2002. http://dx.doi.org/10.1109/icassp.2002.5744012.

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Oraintara. "The generalized discrete fractional Fourier transforms." In IEEE International Conference on Acoustics Speech and Signal Processing ICASSP-02. IEEE, 2002. http://dx.doi.org/10.1109/icassp.2002.1005960.

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Talwalkar, Sumit A., and S. Lawrence Marple. "Time-frequency scaling property of Discrete Fourier Transform (DFT)." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5495902.

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Reports on the topic "Discrete Fourier transforms (DFTs)"

1

Yegulalp, A. F. Asymptotic Error for Windowed Discrete Fourier Transforms. Fort Belvoir, VA: Defense Technical Information Center, August 2006. http://dx.doi.org/10.21236/ada452964.

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Gabriel, William F. Adaptive Digital Processing Investigation of DFT (Discrete Fourier Transform) Subbanding vs. Transversal Filter Canceler. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada171894.

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