Showing papers on "Discrete Fourier transform published in 2011"
TL;DR: In this paper, an enhanced phase-locked loop (EPLL) was used for the estimation of synchrophasors in a phasor measurement unit (PMU) under off-nominal frequency operation.
Abstract: This paper introduces the application of an enhanced phase-locked loop (EPLL) system to the estimation of synchrophasors in a phasor measurement unit (PMU). The major concern is accurate estimation within off-nominal frequency operation of the system. The well-known technique based on discrete Fourier transform (DFT) can provide accurate estimation of the phasors in a three-phase balanced system. However, the negative-sequence component causes errors to the DFT estimates. The DFT cannot accomplish this task in a single-phase system. The EPLL is shown to be a solution for those shortcomings of the DFT technique, both in single-phase and in unbalanced three-phase systems, at the expense of some more complicated structure. Extensive steady-state and dynamic tests are performed and the results are presented and discussed.
162 citations
TL;DR: A watermarking method, which minimizes the impact of the watermark implementation on the overall quality of an image, is developed using a peak signal-to-noise ratio to evaluate quality degradation.
Abstract: In this paper, we evaluate the degradation of an image due to the implementation of a watermark in the frequency domain of the image. As a result, a watermarking method, which minimizes the impact of the watermark implementation on the overall quality of an image, is developed. The watermark is embedded in magnitudes of the Fourier transform. A peak signal-to-noise ratio is used to evaluate quality degradation. The obtained results were used to develop a watermarking strategy that chooses the optimal radius of the implementation to minimize quality degradation. The robustness of the proposed method was evaluated on the dataset of 1000 images. Detection rates and receiver operating characteristic performance showed considerable robustness against the print-scan process, print-cam process, amplitude modulated, halftoning, and attacks from the StirMark benchmark software.
115 citations
Patent•
21 Nov 2011TL;DR: In this article, a method of calculating a Head Media Separation (HMS) from a preamble of embedded servo sectors in a disk drive may include steps of reading the preambles, the read preambled being amplified by a variable gain amplifier (VGA) set at a predetermined gain; transforming samples of the read PREAMBLE into a first and a second frequency using a discrete time-to-frequency domain transform such as a Discrete Fourier Transform (DFT).
Abstract: A method of calculating a Head Media Separation (HMS) from a preamble of embedded servo sectors in a disk drive may include steps of reading the preamble, the read preamble being amplified by a variable gain amplifier (VGA) set at a predetermined gain; transforming samples of the read preamble into a first and a second frequency using a discrete time-to-frequency domain transform such as a Discrete Fourier Transform (DFT); calculating the ratio of the magnitude of the discrete time-to-frequency domain transform of the first frequency to the magnitude of the discrete time-to-frequency domain transform of the second frequency; determining the HMS from the calculated ratio, and enabling the predetermined gain to be updated in synchronism with the transforming step.
105 citations
TL;DR: This paper shows that an image can be decomposed into a sum of a “periodic component” and a ‘smooth component’, which brings a simple and computationally efficient answer to this problem.
Abstract: When the Discrete Fourier Transform of an image is computed, the image is implicitly assumed to be periodic. Since there is no reason for opposite borders to be alike, the "periodic" image generally presents strong discontinuities across the frame border. These edge effects cause several artifacts in the Fourier Transform, in particular a well-known "cross" structure made of high energy coefficients along the axes, which can have strong consequences on image processing or image analysis techniques based on the image spectrum (including interpolation, texture analysis, image quality assessment, etc.). In this paper, we show that an image can be decomposed into a sum of a "periodic component" and a "smooth component", which brings a simple and computationally efficient answer to this problem. We discuss the interest of such a decomposition on several applications.
100 citations
TL;DR: A novel PLL scheme based on a real-time implementation of the discrete Fourier transform (DFT) is presented in this paper and can be considered to be a PLL in which phase detection is performed via a DFT-based algorithm.
Abstract: Phase-locked loop (PLL) algorithms are commonly used to track sinusoidal components in currents and voltage signals in three-phase power systems. Despite the simplicity of those algorithms, problems arise when signals have variable frequency or amplitude, or are polluted with harmonic content and measurement noise, as can be found in aircraft ac power systems where the fundamental frequency can vary in the range 360-900 Hz. To improve the quality of phase and frequency estimates in such power systems, a novel PLL scheme based on a real-time implementation of the discrete Fourier transform (DFT) is presented in this paper. The DFT algorithm calculates the amplitudes of three consecutive components in the frequency domain. These components are used to determine an error signal which is minimized by a proportional-integral loop filter in order to estimate the fundamental frequency. The integral of the estimated frequency is the estimated phase of the fundamental component, and this is fed back to the DFT algorithm. The proposed algorithm can therefore be considered to be a PLL in which phase detection is performed via a DFT-based algorithm. A comparison has been made of the performances of a standard PLL and the proposed DFT-PLL using computer simulations and through experiments.
99 citations
01 Dec 2011
TL;DR: An approach for providing important feedback information about weld quality in real-time to a control system for friction stir welding using the discrete Fourier transform and a multilayer neural network is demonstrated.
Abstract: This paper introduces a novel real-time approach to detecting wormhole defects in friction stir welding in a nondestructive manner. The approach is to evaluate feedback forces provided by the welding process using the discrete Fourier transform and a multilayer neural network. It is asserted here that the oscillations of the feedback forces are related to the dynamics of the plasticized material flow, so that the frequency spectra of the feedback forces can be used for detecting wormhole defects. A one-hidden-layer neural network trained with the backpropagation algorithm is used for classifying the frequency patterns of the feedback forces. The neural network is trained and optimized with a data set of forge-load control welds, and the generality is tested with novel data set of position control welds. Overall, about 95% classification accuracy is achieved with no bad welds classified as good. Accordingly, the present paper demonstrates an approach for providing important feedback information about weld quality in real-time to a control system for friction stir welding.
94 citations
TL;DR: Techniques for sense through wall human detection for different types of walls based on breathing movements and a new approach based on short time Fourier transform is discussed.
Abstract: In this article, we discuss techniques for sense through wall human detection for different types of walls. We have focused on detection of stationary human target behind wall based on breathing movements. In detecting the breathing motion, a Doppler based method is used. Also a new approach based on short time Fourier transform is discussed and an already proposed clutter reduction technique based on singular value decomposition is applied to different measurements.
91 citations
TL;DR: In this paper, a sensorless controller for an interior permanent-magnet synchronous motor is presented based on well-known high-frequency signal injection techniques, and the issue of the demodulation process is the key point of this paper.
Abstract: In this paper, a sensorless controller for an interior permanent-magnet synchronous motor is presented based on well-known high-frequency signal injection techniques. The issue of the demodulation process is the key point of this paper. A novel approach based on discrete Fourier transform and nonconventional reference frame transformation is presented, allowing a simple and robust noncoherent demodulation, i.e., in which no information about the carrier phase is needed. In the classically adopted coherent approaches, in fact, uncertainty about carrier phase reflects in uncertainty in the demodulated signal amplitude, affecting observer gains and signal-to-noise ratio and definitively providing a degradation of the performance of the estimator. Analytical development of the sensorless algorithm, including the demodulation technique, is provided. A complete investigation by simulation is carried out aiming at showing the performance of the proposed method. Finally, experimental results are presented based on a prototype motor drive for city scooters.
87 citations
TL;DR: The results show that the property of a Boolean function having a concise Fourier representation is locally testable and an “implicit learning” algorithm is given that lets us test any subproperty of Fourier concision.
Abstract: We present a range of new results for testing properties of Boolean functions that are defined in terms of the Fourier spectrum. Broadly speaking, our results show that the property of a Boolean function having a concise Fourier representation is locally testable. We give the first efficient algorithms for testing whether a Boolean function has a sparse Fourier spectrum (small number of nonzero coefficients) and for testing whether the Fourier spectrum of a Boolean function is supported in a low-dimensional subspace of $\mathbb{F}_2^n$. In both cases we also prove lower bounds showing that any testing algorithm—even an adaptive one—must have query complexity within a polynomial factor of our algorithms, which are nonadaptive. Building on these results, we give an “implicit learning” algorithm that lets us test any subproperty of Fourier concision. We also present some applications of these results to exact learning and decoding. Our technical contributions include new structural results about sparse Boolean functions and new analysis of the pairwise independent hashing of Fourier coefficients from [V. Feldman, P. Gopalan, S. Khot, and A. Ponnuswami, Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2006, pp. 563-576].
85 citations
TL;DR: This paper describes the discrete Fourier transform interpolation algorithm for arbitrary windows and its application and performance for optimal noncosine Kaiser-Bessel and Dolph-Chebyshev windows.
Abstract: This paper describes the discrete Fourier transform (DFT) interpolation algorithm for arbitrary windows and its application and performance for optimal noncosine Kaiser-Bessel and Dolph-Chebyshev windows. The interpolation algorithm is based on the polynomial approximation of the window's spectrum that is computed numerically. Two- and three-point (2p and 3p) interpolations are considered. Systematic errors and noise sensitivity are analyzed for the chosen Kaiser-Bessel and Dolph-Chebyshev windows and compared with Rife-Vincent class I windows.
81 citations
TL;DR: The aim of this monograph is to clarify the role of Fourier Transforms in the development of Functions of Complex Numbers and to propose a procedure called the Radon Transform, which is based on the straightforward transformation of the Tournaisian transform.
Abstract: Series Editor s Preface. Preface. 1 Introduction. 1.1 Signals, Operators, and Imaging Systems. 1.2 The Three Imaging Tasks. 1.3 Examples of Optical Imaging. 1.4 ImagingTasks inMedical Imaging. 2 Operators and Functions. 2.1 Classes of Imaging Operators. 2.2 Continuous and Discrete Functions. Problems. 3 Vectors with Real-Valued Components. 3.1 Scalar Products. 3.2 Matrices. 3.3 Vector Spaces. Problems. 4 Complex Numbers and Functions. 4.1 Arithmetic of Complex Numbers. 4.2 Graphical Representation of Complex Numbers. 4.3 Complex Functions. 4.4 Generalized Spatial Frequency Negative Frequencies. 4.5 Argand Diagrams of Complex-Valued Functions. Problems. 5 Complex-Valued Matrices and Systems. 5.1 Vectors with Complex-Valued Components. 5.2 Matrix Analogues of Shift-Invariant Systems. 5.3 Matrix Formulation of ImagingTasks. 5.4 Continuous Analogues of Vector Operations. Problems. 6 1-D Special Functions. 6.1 Definitions of 1-D Special Functions. 6.2 1-D Dirac Delta Function. 6.3 1-D Complex-Valued Special Functions. 6.4 1-D Stochastic Functions Noise. 6.5 Appendix A: Area of SINC[x] and SINC2[x]. 6.6 Appendix B: Series Solutions for Bessel Functions J0[x] and J1[x]. Problems. 7 2-D Special Functions. 7.1 2-D Separable Functions. 7.2 Definitions of 2-D Special Functions. 7.3 2-D Dirac Delta Function and its Relatives. 7.4 2-D Functions with Circular Symmetry. 7.5 Complex-Valued 2-D Functions. 7.6 Special Functions of Three (orMore) Variables. Problems. 8 Linear Operators. 8.1 Linear Operators. 8.2 Shift-Invariant.Operators. 8.3 Linear Shift-Invariant (LSI) Operators. 8.4 Calculating Convolutions. 8.5 Properties of Convolutions. 8.6 Autocorrelation. 8.7 Crosscorrelation. 8.8 2-DLSIOperations. 8.9 Crosscorrelations of 2-D Functions. 8.10 Autocorrelations of 2-D.Functions. Problems. 9 Fourier Transforms of 1-D Functions. 9.1 Transforms of Continuous-Domain Functions. 9.2 Linear Combinations of Reference Functions. 9.3 Complex-Valued Reference Functions. 9.4 Transforms of Complex-Valued Functions. 9.5 Fourier Analysis of Dirac Delta Functions. 9.6 Inverse Fourier Transform. 9.7 Fourier Transforms of 1-D Special Functions. 9.8 Theorems of the Fourier Transform. 9.9 Appendix: Spectrum of Gaussian via Path Integral. Problems. 10 Multidimensional Fourier Transforms. 10.1 2-D Fourier Transforms. 10.2 Spectra of Separable 2-D Functions. 10.3 Theorems of 2-D Fourier Transforms. Problems. 11 Spectra of Circular Functions. 11.1 The Hankel Transform. 11.2 Inverse Hankel Transform. 11.3 Theorems of Hankel Transforms. 11.4 Hankel Transforms of Special Functions. 11.5 Appendix: Derivations of Equations (11.12) and (11.14). Problems. 12 The Radon Transform. 12.1 Line-Integral Projections onto Radial Axes. 12.2 Radon Transforms of Special Functions. 12.3 Theorems of the Radon Transform. 12.4 Inverse Radon Transform. 12.5 Central-Slice Transform. 12.6 Three Transforms of Four Functions. 12.7 Fourier and Radon Transforms of Images. Problems. 13 Approximations to Fourier Transforms. 13.1 Moment Theorem. 13.2 1-D Spectra via Method of Stationary Phase. 13.3 Central-Limit Theorem. 13.4 Width Metrics and Uncertainty Relations. Problems. 14 Discrete Systems, Sampling, and Quantization. 14.1 Ideal Sampling. 14.2 Ideal Sampling of Special Functions. 14.3 Interpolation of Sampled Functions. 14.4 Whittaker Shannon Sampling Theorem. 14.5 Aliasingand Interpolation. 14.6 Prefiltering to Prevent Aliasing. 14.7 Realistic Sampling. 14.8 Realistic Interpolation. 14.9 Quantization. 14.10 Discrete Convolution. Problems. 15 Discrete Fourier Transforms. 15.1 Inverse of the Infinite-Support DFT. 15.2 DFT over Finite Interval. 15.3 Fourier Series Derived from Fourier Transform. 15.4 Efficient Evaluation of the Finite DFT. 15.5 Practical Considerations for DFT and FFT. 15.6 FFTs of 2-D Arrays. 15.7 Discrete Cosine Transform. Problems. 16 Magnitude Filtering. 16.1 Classes of Filters. 16.2 Eigenfunctions of Convolution. 16.3 Power Transmission of Filters. 16.4 Lowpass Filters. 16.5 Highpass Filters. 16.6 Bandpass Filters. 16.7 Fourier Transform as a Bandpass Filter. 16.8 Bandboost and Bandstop Filters. 16.9 Wavelet Transform. Problems. 17 Allpass (Phase) Filters. 17.1 Power-Series Expansion for Allpass Filters. 17.2 Constant-Phase Allpass Filter. 17.3 Linear-Phase Allpass Filter. 17.4 Quadratic-Phase Filter. 17.5 Allpass Filters with Higher-Order Phase. 17.6 Allpass Random-Phase Filter. 17.7 Relative Importance of Magnitude and Phase. 17.8 Imaging of Phase Objects. 17.9 Chirp Fourier Transform. Problems. 18 Magnitude Phase Filters. 18.1 Transfer Functions of Three Operations. 18.2 Fourier Transform of Ramp Function. 18.3 Causal Filters. 18.4 Damped Harmonic Oscillator. 18.5 Mixed Filters with Linear or Random Phase. 18.6 Mixed Filter with Quadratic Phase. Problems. 19 Applications of Linear Filters. 19.1 Linear Filters for the Imaging Tasks. 19.2 Deconvolution Inverse Filtering . 19.3 Optimum Estimators for Signals in Noise. 19.4 Detection of Known Signals Matched Filter. 19.5 Analogies of Inverse and Matched Filters. 19.6 Approximations to Reciprocal Filters. 19.7 Inverse Filtering of Shift-Variant Blur. Problems. 20 Filtering in Discrete Systems. 20.1 Translation, Leakage, and Interpolation. 20.2 Averaging Operators Lowpass Filters. 20.3 Differencing Operators Highpass Filters. 20.4 Discrete Sharpening Operators. 20.5 2-DGradient. 20.6 Pattern Matching. 20.7 Approximate Discrete Reciprocal Filters. Problems. 21 Optical Imaging in Monochromatic Light. 21.1 Imaging Systems Based on Ray Optics Model. 21.2 Mathematical Model of Light Propagation. 21.3 Fraunhofer Diffraction. 21.4 Imaging System based on Fraunhofer Diffraction. 21.5 Transmissive Optical Elements. 21.6 Monochromatic Optical Systems. 21.7 Shift-Variant Imaging Systems. Problems. 22 Incoherent Optical Imaging Systems. 22.1 Coherence. 22.2 Polychromatic Source Temporal Coherence. 22.3 Imaging in Incoherent Light. 22.4 System Function in Incoherent Light. Problems. 23 Holography. 23.1 Fraunhofer Holography. 23.2 Holography in Fresnel Diffraction Region. 23.3 Computer-Generated Holography. 23.4 Matched Filtering with Cell-Type CGH. 23.5 Synthetic-Aperture Radar (SAR). Problems. References. Index.
TL;DR: A new DFT interpolation algorithm is derived for a signal analyzed with Rife-Vincent class-I windows and new formulas that extend Bertocco and Yoshida methods for resonant frequency and logarithmic decrement estimation are proposed.
Abstract: In this paper, we analyze and compare the properties of different well-known and also new nonparametric discrete Fourier transform (DFT)-based methods for resonant frequency and logarithmic decrement estimation in application to mechanical spectroscopy. We derive a new DFT interpolation algorithm for a signal analyzed with Rife-Vincent class-I windows and also propose new formulas that extend Bertocco and Yoshida methods. We study errors of the resonant frequency and logarithmic decrement estimation in realistic conditions that include measurement noise and a zero-point drift. We also investigate the systematic errors of the estimation methods of interest. A nonlinear least squares time-domain parametric signal fitting is used to determine the boundaries of statistical efficiency in all tests.
TL;DR: This work shows that the fast Fourier transform, so called hyperbolic cross FFT, suffers from an increase of its condition number for both increasing refinement and increasing spatial dimension.
Abstract: A straightforward discretisation of problems in high dimensions often leads to an exponential growth in the number of degrees of freedom. Sparse grid approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives and the fast Fourier transform (FFT) has been adapted to this thin discretisation. We show that this so called hyperbolic cross FFT suffers from an increase of its condition number for both increasing refinement and increasing spatial dimension.
TL;DR: Fast Fourier transform (FFT) algorithm can be introduced into the calculation of convolution format of gyrator transform in the discrete case by using convolution operation.
28 Jan 2011
TL;DR: When compared, Discrete Cosine Transform and Fast Fourier Transform give better compression ratio, while Discrete Wavelet Transform yields good fidelity parameters with comparable compression ratio.
Abstract: In this paper, a transform based methodology is presented for compression of electrocardiogram (ECG) signal. The methodology employs different transforms such as Discrete Wavelet Transform (DWT), Fast Fourier Transform (FFT) and Discrete Cosine Transform (DCT). A comparative study of performance of different transforms for ECG signal is made in terms of Compression ratio (CR), Percent root mean square difference (PRD), Mean square error (MSE), Maximum error (ME) and Signal-to-noise ratio (SNR). The simulation results included illustrate the effectiveness of these transforms in biomedical signal processing. When compared, Discrete Cosine Transform and Fast Fourier Transform give better compression ratio, while Discrete Wavelet Transform yields good fidelity parameters with comparable compression ratio.
TL;DR: A new multicarrier system using a low computational complexity transform that combines the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT) into a single fast orthonormal unitary transform, leading to a significant improvement in bit error rate (BER) and reasonable reduction in the peak-to-average power ratio (PAPR).
Abstract: This paper introduces a new multicarrier system using a low computational complexity transform that combines the Walsh-Hadamard transform (WHT) and the discrete Fourier transform (DFT) into a single fast orthonormal unitary transform. The proposed transform is used in a new orthogonal frequency division multiplexing ( T-OFDM) system, leading to a significant improvement in bit error rate (BER) and reasonable reduction in the peak-to-average power ratio (PAPR). Use of the proposed transform with OFDM has been found to attain high frequency diversity gain by combining all data samples resulting in the transmission over many subcarriers. Consequently, the detrimental effect arising from channel fading on the subcarrier power is minimized. Theoretical analysis of the uncoded T-OFDM performance over additive white Gaussian noise (AWGN), flat fading, quasi-static (fixed within the entire period of OFDM symbol transmission) frequency selective fading channel models with zero-forcing (ZF) and minimum mean square error (MMSE) equalizers is presented in this work. Moreover, the low superposition of the subcarriers passing through the T-transforms leads to a reduction in the high peak of the transmitted signal whilst preserving the average transmitted power and data rate. Analytical results confirmed by simulations demonstrated that the proposed T-OFDM system achieves lower PAPR and the same BER over AWGN and flat fading channels. Compared to OFDM, T-OFDM is found to have better BER when MMSE equalizer is used, but slightly worse when ZF equalizer is used.
TL;DR: In this article, the modified harmonic domain and the modified dynamic harmonic domain are proposed for calculating steady and dynamic states, respectively. But the main difference is the inclusion of interharmonics in either steady or dynamic state.
Abstract: This paper presents the basics of two techniques, named here as the modified harmonic domain and the modified dynamic harmonic domain, proposed for calculating steady and dynamic states, respectively. These techniques have their fundamental in the harmonic domain with a substantial improvement: the inclusion of interharmonics in either steady or dynamic state. This is performed through the use of the discrete Fourier transform which allows an arbitrary frequency-domain discretization, thus permitting the representation of interharmonics.
TL;DR: In this article, a real-time classification method of power quality (PQ) disturbances is proposed. But the proposed method is limited to the detection and classification of nine types of PQ disturbances.
TL;DR: This paper accounts for the information rate, memory, power efficiency, bit error rate (BER) performance and spectral occupancy of CPM-SC-FDMA, a novel multiple-access modulation scheme which combines key characteristics of single carrier frequency division multiple access with continuous phase modulation in order to generate a power efficient waveform.
Abstract: This paper presents a novel multiple-access modulation scheme which combines key characteristics of single carrier frequency division multiple access (SC-FDMA) with continuous phase modulation (CPM) in order to generate a power efficient waveform. CPM-SC-FDMA is developed based upon the observation that the samples from a CPM waveform may be treated as "data symbols" taken from a constant-envelope encoder. As with any encoder output, these samples may be precoded using the Discrete Fourier Transform and transmitted using SC-FDMA. Having originated from a constant envelope CPM waveform, CPM-SC-FDMA can potentially retain much of the power efficiency of CPM-thus resulting in a lower peak-to-average power ratio (PAPR) than conventional SC-FDMA. In this paper, we account for the information rate, memory, power efficiency, bit error rate (BER) performance and spectral occupancy of CPM-SC-FDMA. In addition, we investigate the impact of amplifier nonlinearity on BER performance as the number of users increases. Finally, we provide a detailed numerical comparison with a commensurate convolutionally coded QPSK-SC-FDMA scheme (CC-QPSK-SC-FDMA). We show a CPM-SC-FDMA scheme that provides an overall gain of up to 4 dB relative to the CC-QPSK-SC-FDMA scheme over a frequency-selective channel.
TL;DR: This paper presents a new approach for denoising sensor signals using the Empirical Mode Decomposition (EMD) technique and the Information-theoretic method, and finds that it performs better than DWT and DFT in most cases, and comparatively to DWT in some cases in terms of: 1) mean square error; 2) recomputed signal-to-noise ratio; and 3) visual quality of the denoised signals.
Abstract: This paper presents a new approach for denoising sensor signals using the Empirical Mode Decomposition (EMD) technique and the Information-theoretic method. The EMD technique is applied to decompose a noisy sensor signal into the so-called intrinsic mode functions (IMFs). These functions are of the same length and in the same time domain as the original signal. Therefore, the EMD technique preserves varying frequency in time. Assuming the given signal is corrupted by high-frequency (HF) Gaussian noise implies that most of the noise should be captured by the first few modes. Therefore, our proposition is to separate the modes into HF and low-frequency (LF) groups. We applied an information-theoretic method, namely, mutual information to determine the cutoff for separating the modes. A denoising procedure is applied only to the HF group using a shrinkage approach. Upon denoising, this group is combined with the original LF group to obtain the overall denoised signal. We illustrate our approach with simulated and real-world cargo radiation data sets. The results are compared to two popular denoising techniques in the literature, namely discrete Fourier transform (DFT) and discrete wavelet transform (DWT). We found that our approach performs better than DWT and DFT in most cases, and comparatively to DWT in some cases in terms of: 1) mean square error; 2) recomputed signal-to-noise ratio; and 3) visual quality of the denoised signals.
TL;DR: A noisy speech enhancement method by combining linear prediction (LP) residual weighting in the time domain and spectral processing in the frequency domain to provide better noise suppression as well as better enhancement in the speech regions is presented.
TL;DR: A novel multi-image encryption and decryption algorithm based on Fourier transform and fractional Fourier transforms that has features of enhancement in decryption accuracy and high optical efficiency is presented.
TL;DR: A novel decoupling of the least-squares problem is demonstrated which results in two systems of equations, one of which may be solved quickly by means of fast Fourier transforms (FFTs) and another that is demonstrated to be well approximated by a low-rank system.
Abstract: A new algorithm is presented which provides a fast method for the computation of recently developed Fourier continuations (a particular type of Fourier extension method) that yield superalgebraically convergent Fourier series approximations of nonperiodic functions. Previously, the coefficients of an approximating Fourier series have been obtained by means of a regularized singular value decomposition (SVD)-based least-squares solution to an overdetermined linear system of equations. These SVD methods are effective when the size of the system does not become too large, but they quickly become unwieldy as the number of unknowns in the system grows. We demonstrate a novel decoupling of the least-squares problem which results in two systems of equations, one of which may be solved quickly by means of fast Fourier transforms (FFTs) and another that is demonstrated to be well approximated by a low-rank system. Utilizing randomized algorithms, the low-rank system is reduced to a significantly smaller system of equations. This new system is then efficiently solved with drastically reduced computational cost and memory requirements while still benefiting from the advantages of using a regularized SVD. The computational cost of the new algorithm in on the order of the cost of a single FFT multiplied by a slowly increasing factor that grows only logarithmically with the size of the system.
TL;DR: In this article, the authors define the quadratic algebra which is a one-parameter deformation of the Lie algebra extended by a parity operator, and investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra.
Abstract: We define the quadratic algebra which is a one-parameter deformation of the Lie algebra extended by a parity operator. The odd-dimensional representations of (with representation label j, a positive integer) can be extended to representations of . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier–Hahn transform is computed explicitly. The matrix of this discrete Fourier–Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform.
TL;DR: In this paper, the natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT) via the finite difference method under the simple support boundary condition.
Abstract: Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform of a series of data samples by means of digital computers. The governing equations of coupled planar of an axially moving beam are reduced to two nonlinear models of transverse vibration. Numerical schemes are respectively presented for the governing equations via the finite difference method under the simple support boundary condition. In this paper, time series of the discrete Fourier transform is defined as numerically solutions of three nonlinear governing equations, respectively. The standard FFT scheme is used to investigate the natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results are compared with the first two natural frequencies of linear free transverse vibration of an axially moving beam. And results indicate that the effect of the nonlinear coefficient on the first natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results also illustrate the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters.
TL;DR: This paper test the use of the periodicity representations alone, combined with tempo information and combined with a proposed set of rhythm features to achieve high recognition rates at least comparable to previously published results.
Abstract: In this paper, we study the spectral and temporal periodicity representations that can be used to describe the characteristics of the rhythm of a music audio signal. A continuous-valued energy-function representing the onset positions over time is first extracted from the audio signal. From this function we compute at each time a vector which represents the characteristics of the local rhythm. Four feature sets are studied for this vector. They are derived from the amplitude of the discrete Fourier transform (DFT), the auto-correlation function (ACF), the product of the DFT and the ACF interpolated on a hybrid lag/frequency axis and the concatenated DFT and ACF coefficients. Then the vectors are sampled at some specific frequencies, which represent various ratios of the local tempo. The ability of these periodicity representations to describe the rhythm characteristics of an audio item is evaluated through a classification task. In this, we test the use of the periodicity representations alone, combined with tempo information and combined with a proposed set of rhythm features. The evaluation is performed using annotated and estimated tempo. We show that using such simple periodicity representations allows achieving high recognition rates at least comparable to previously published results.
Patent•
25 Oct 2011TL;DR: In this paper, a wireless communication receiver including a serial to parallel converter receiving an radio frequency signal, a fast Fourier transform device connected to a serial-to-parallel converter converting N FFT corresponding serial signals into a frequency domain; an EZC root sequence unit generating a set of root sequence signals; an element-by-element multiply unit forming an set of products including a product of each of said frequency domain signals from said fast-fraction transform device and a corresponding root sequence signal, an N SRS -length IDFT unit performing a group cyclic-
Abstract: A wireless communication receiver including a serial to parallel converter receiving an radio frequency signal, a fast Fourier transform device connected to said serial to parallel converter converting N FFT corresponding serial signals into a frequency domain; an EZC root sequence unit generating a set of root sequence signals; an element-by-element multiply unit forming a set of products including a product of each of said frequency domain signals from said fast Fourier transform device and a corresponding root sequence signal, an N SRS -length IDFT unit performing a group cyclic-shift de-multiplexing of the products and a discrete Fourier transform unit converting connected cyclic shift de-multiplexing signals back to frequency-domain
TL;DR: A new effective method for image encryption which employs magnitude and phase manipulation using Differential Evolution (DE) approach and the resulting encrypted image is found to be fully distorted, resulting in increasing the robustness of the proposed work.
Abstract: This paper presents a new effective method for image encryption which employs magnitude and phase manipulation using Differential Evolution (DE) approach. The novelty of this work lies in deploying the concept of keyed discrete Fourier transform (DFT) followed by DE operations for encryption purpose. To this end, a secret key is shared between both encryption and decryption sides. Firstly two dimensional (2-D) keyed discrete Fourier transform is carried out on the original image to be encrypted. Secondly crossover is performed between two components of the encrypted image, which are selected based on Linear Feedback Shift Register (LFSR) index generator. Similarly, keyed mutation is performed on the real parts of a certain components selected based on LFSR index generator. The LFSR index generator initializes it seed with the shared secret key to ensure the security of the resulting indices. The process shuffles the positions of image pixels. A new image encryption scheme based on the DE approach is developed which is composed with a simple diffusion mechanism. The deciphering process is an invertible process using the same key. The resulting encrypted image is found to be fully distorted, resulting in increasing the robustness of the proposed work. The simulation results validate the proposed image encryption scheme.
TL;DR: The problem of estimating the frequency of a complex single tone is considered and two iterative Fourier interpolation algorithms are generalized by introducing an additional parameter to allow for selection of the Fouriers interpolation coefficients relative to the true frequency.
TL;DR: It is shown that the selective DFT attack is more efficient than known methods for the case when the number of observed consecutive bits of a filter generator is less than the linear complexity of the sequence.
Abstract: In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the Ronjom-Helleseth attack and the modifications due to Ronjom, Gong, and Helleseth. The first part of this paper fills some gaps in the theory of analysis in terms of the discrete Fourier transform (DFT). The second part introduces the new fast selective DFT attacks, which are closely related to the fast algebraic attacks in the literature. However, in contrast to the classical view that successful algebraic cryptanalysis of LFSR-based stream cipher depends on the degree of certain annihilators, the analysis in terms of the DFT spectral properties of the sequences generated by these functions is far more refined. It is shown that the selective DFT attack is more efficient than known methods for the case when the number of observed consecutive bits of a filter generator is less than the linear complexity of the sequence. Thus, by utilizing the natural representation imposed by the underlying LFSRs, in certain cases, the analysis in terms of DFT spectra is more efficient and has more flexibility than classical and fast algebraic attacks. Consequently, the new attack imposes a new criterion for the design of cryptographic strong Boolean functions, which is defined as the spectral immunity of a sequence or a Boolean function.