Showing papers on "Discrete-time Fourier transform published in 2004"

Detection and parameter estimation of multicomponent LFM signal based on the fractional Fourier transform

Abstract: This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.

Extended heat-fluctuation theorems for a system with deterministic and stochastic forces.

Abstract: Heat fluctuations over a time tau in a nonequilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.

The truncated fourier transform and applications

Abstract: In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the "jumps" in the complexity at powers of two. When applied to the multiplication of multivariate polynomials or truncated multivariate power series, we gain a logarithmic factor with respect to the best previously known algorithms.

Nonlinear Microwave Circuit Design

Abstract: Preface.Chapter 1. Nonlinear Analysis Methods.1.1 Introduction.1.2 Time-Domain Solution.1.3 Solution Through Series Expansion1.4 The Conversion Matrix.1.5 Bibliography.Chapter 2. Nonlinear Measurements.2.1 Introduction.2.2 Load/Source-Pull.2.3 The Vector Nonlinear Network Analyser.2.4 Pulsed Measurements.2.5 Bibliography.Chapter 3. Nonlinear Models.3.1 Introduction.3.2 Physical Models.3.3 Equivalent-Circuit Models.3.4 Black-Box Models.3.5 Simplified Models.3.6 Bibliography.Chapter 4. Power Amplifiers.4.1 Introduction.4.2 Classes of Operation.4.3 Simplified Class-A Fundamental-Frequency Design For High Efficiency.4.4 Multi-Harmonic Design For High Power And Efficiency.4.5 Bibliography.Chapter 5. Oscillators.5.1 Introduction.5.2 Linear Stability and Oscillation Conditions.5.3 From Linear To Nonlinear: Quasi-Large-Signal Oscillation And Stability Conditions.5.4 Design Methods.5.5 Nonlinear Analysis Methods For Oscillators.5.6 Noise.5.7 Bibliography.Chapter 6. Frequency Multipliers and Dividers.6.1 Introduction.6.2 Passive Multipliers.6.3 Active Multipliers.6.4 Frequency Dividers-The Rigenerative (Passive) Approach.6.5 Bibliography.Chapter 7. Mixers. 7.1 Introduction.7.2 Mixer Configurations.7.3 Mixer Design.7.4 Nonlinear Analysis.7.5 Noise.7.6 Bibliography.Chapter 8. Stability and Injection-locked Circuits.8.1 Introduction.8.2 Local Stability Of Nonlinear Circuits In Large-Signal Regime.8.3 Nonlinear Analysis, Stability And Bifurcations.8.4 Injection Locking.8.5 Bibliography.Appendix.A.1. Transformation in the Fourier Domain of the Linear Differential Equation.A.2. Time-Frequency Transformations.A.3 Generalized Fourier Transformation for the Volterra Series Expansion.A.4 Discrete Fourier Transform and Inverse Discrete Fourier Transform for Periodic Signals.A.5 The Harmonic Balance System of Equations for the Example Circuit with N=3.A.6 The Jacobian MatrixA.7 Multi-dimensional Discrete Fourier Transform and Inverse Discrete Fourier Transform for quasi-periodic signals.A.8 Oversampled Discrete Fourier Transform and Inverse Discrete Fourier Transform for Quasi-Periodic Signals.A.9 Derivation of Simplified Transport Equations.A.10 Determination of the Stability of a Linear Network.A.11 Determination of the Locking Range of an Injection-Locked Oscillator.Index.

Application of Fourier transform and autocorrelation to cluster identification in the three-dimensional atom probe

Abstract: Because of the increasing number of collected atoms (up to millions) in the three-dimensional atom probe, derivation of chemical or structural information from the direct observation of three-dimensional images is becoming more and more difficult. New data analysis tools are thus required. Application of a discrete Fourier transform algorithm to three-dimensional atom probe datasets provides information that is not easily accessible in real space. Derivation of mean particle size from Fourier intensities or from three-dimensional autocorrelation is an example. These powerful methods can be used to detect and image nano-segregations. Using three-dimensional 'bright-field' imaging, single nano-segregations were isolated from the surrounding matrix of an iron-copper alloy. Measurement of the inner concentration within clusters is, therefore, straightforward. Theoretical aspects related to filtering in reciprocal space are developed.

Robust and frequency-adaptive measurement of peak value

Abstract: A new approach for measuring the peak value of the fundamental component of a distorted sinusoidal signal for power system applications is presented. The method is applicable to single-phase as well as three-phase systems. While maintaining structural simplicity, the proposed approach is highly robust with respect to noise and distortion due to disturbances and unbalanced conditions of the system. The method is also highly tolerant of uncertainties in the setting of its internal parameters. The salient feature of the proposed approach is its capability of adapting to the variations in the center frequency of the input signal. The method is suitable for environments that frequency excursions are experienced and conventional discrete Fourier transform (DFT)-based methods do not provide satisfactory results. Speed and accuracy of the response can also be controlled. Structural simplicity and robustness of the proposed scheme make it well suited for digital implementation on software and hardware platforms. Performance of the proposed method is presented based on simulation studies in the MATLAB environment and an experimental setup.

Fourier embeddings and Mihlin‐type multiplier theorems

Abstract: Recent theorems on singular convolution operators are combined with new Fourier embedding results to prove strong multiplier theorems on various function spaces (including Besov, Lebesgue–Bochner, and Hardy). All the results apply to operator-valued multipliers acting on vector-valued functions, but some of them are new even in the scalar case. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Windowed Fourier transform method for demodulation of carrier fringes

Abstract: The Fourier transform method for demodulation of carrier fringes has been extensively developed and widely used in optical metrology. However, the Fourier transform being a global operation, it has poor ability to localize the signal properties and hence the result of FTM is not ideal. A windowed Fourier transform method is thus proposed, with advantages of signal localization and noise filtering. An example demonstrates the improved result compared to the traditional Fourier transform.

OFDM signal receiving apparatus and OFDM signal receiving method

Abstract: An OFDM signal receiver reduces frequency response estimation error, and reduces the circuit scale needed for a hardware implementation and the number of operations performed in a software implementation. A first Fourier transform circuit converts an OFDM signal to the frequency domain by a Fourier transform. A first divider divides the pilot signal contained in the frequency domain OFDM signal by a specified pilot signal. A zero insertion means then inserts zero signals in the first divider output. A window function multiplying means multiplies the zero insertion means output by a window function, and an inverse Fourier transform means applies an inverse Fourier transform to the multiplier output. A coring means then cores the inverse Fourier transform output, and truncation means truncates the coring means output at a specified data length. A second Fourier transform circuit applies another Fourier transform to the truncated result. A window function dividing means then divides the Fourier transform result by the window function, and a second dividing means divides the output of the first Fourier transform means by the output of the window function dividing means.

Sub-pixel registration and estimation of local shifts directly in the Fourier domain

Abstract: In this paper, we propose a new approach to sub-pixel registration, and the estimation of local shifts between a pair of images, directly in the Fourier domain. For this purpose, we establish the exact relationship between the continuous and the discrete Fourier phase of two shifted images or their subregions. In particular, we show that the discrete phase difference of two shifted images is a 2-dimensional sawtooth signal, with the exact shifts determined to sub-pixel accuracy by the number of periods of the phase difference along each frequency axis. The sub-pixel portions of the shifts are determined by the non-integer fraction of a period of the phase difference.

Limitations of the potential step technique to impedance measurements using discrete time Fourier transform

Abstract: Recently, a new method of measuring impedance of electrochemical systems was proposed in the literature by Yoo and Park (Yoo, J.-S.; Park, S.-M. Anal. Chem. 2000, 72, 2035). It is based on the analysis of system response to a potential step. Differentiation of the applied potential step and the current response in the time domain followed by applying Fourier transform to both signals allows for determination of the system's impedance. It has been proposed that the measurements carried out in a short time period permit the determination of the system's impedance in the whole frequency range. The aim of the present work was to verify the validity of the impedance spectra obtained using this method, as well as to establish the conditions for which the method may be used. This method was tested using simulated data for a simple ideally polarized electrode and a simple one-electron redox system in the solution. The results show that the reliable impedance spectra may be obtained only for frequencies between 1/...

Improved fast fractional-Fourier-transform algorithm.

Abstract: Through the optimization of the main interval of the fractional order, an improved fast algorithm for numerical calculation of the fractional Fourier transforms is proposed. With this improved algorithm, the fractional Fourier transforms of a rectangular function and a Gaussian function are calculated. Its calculation errors are compared with those calculated with the previously published algorithm, and the results show that the calculation accuracy of the improved algorithm is much higher.

Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations

Abstract: The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily bandlimited, periodic masks at some specific distances.

Identification and location of hot spots in proteins using the short-time discrete Fourier transform

Abstract: A new approach for the identification and location of hot spots in proteins based on the short-time discrete Fourier transform (DFT) is proposed. In the new approach the short-time DFT of the protein numerical sequence is first computed and its columns are then multiplied by the DFT coefficients. By performing this step, the hot spot locations can be clearly identified by distinct peaks in the spectrum, thus achieving good localization in the amino acid domain.

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

Abstract: A versatile method is described for the practical computation of the exact discrete Fourier transforms (DFT), both the direct and the inverse ones, of a continuous function g given by its values gj at the points of a uniform grid FN generated by conjugacy classes of elements of finite adjoint order N in the fundamental region F of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when F is reduced to a one-dimensional segment, and for SU(2)×SU(2)×⋯×SU(2) in multidimensional cases. This simplest case turns out to be a version of the discrete cosine transform (DCT). Implementations, abbreviated as DGT for Discrete Group Transform, based on simple Lie groups of higher ranks, are to be considered separately. DCT is often taken to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of the two inverse discrete transforms are studied. The following properties of the continuous extension of DCT (called CEDCT) from the discrete tj∈FN to all t∈F are proven and exemplified. Like the standard DFT, the DCT also returns the exact values of {gj} on the N+1 points of the grid. However, unlike the continuous extension of the standard DFT: (a) The CEDCT function fN(t) closely approximates g(t) between the points of the grid as well; (b) for increasing N, the derivative of fN(t) converges to the derivative of g(t); (c) for CEDCT the principle of locality is valid. In this article we also use the continuous extension of the two-dimensional (2D) DCT, SU(2)×SU(2), to illustrate its potential for interpolation as well as for the data compression of 2D images.

Fourier analysis of the sampling characteristics of the phase-shifting algorithm

Abstract: In this paper, we analyze the phase-shifting algorithm by utilizing Fourier transformation theory. In fact, the phase-shifting algorithm is corresponding to a discrete Fourier transformation (DFT), the image capturing operation is a temporal sampling procedure, and the purpose of phase-shifting technique is to retrieve the phase of one frequency component. According to the sampling theory, if the number of phase steps is too less that means a too low sampling frequency is adopted, the frequency of interest will be mixed with high order spectra. By mathematical analysis, the relationship between the number of phase steps and the effect of harmonics is deduced, and the criterion of selecting phase step number is discussed. The applications of the Fourier analysis in digital fringe projection profilometry are described.

Comments on Hilbert Transform Based Signal Analysis

Abstract: The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is the basis of the Discrete Fourier Transform [DFT]) since any other interpretation is inconsistent. A simple derivation of the Hilbert transform for a sampled, periodic is then given. It is shown that the instantaneous frequency can be easily computed from the Discrete Fourier Series (or, equivalently, the DFT) representation of the signal. Since this representation is exact, the Hilbert transform representation is also exact.

An algebraic approach to symmetry detection

Abstract: We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.

Fourier fringe processing by use of an interpolated Fourier-transform technique

Abstract: Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

Abstract: A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

Filtering of chirped ultrasound echo signals with the fractional Fourier transform

Abstract: The fractional Fourier transform represents a generalisation of the conventional Fourier transform. Previous work (M. Bennett et al, Proc. IEEE EMBS vol. 1, pp. 882-885, 2003) has shown that the application of the fractional Fourier transform to conventional, un-coded ultrasound signals has little advantage over conventional filtering techniques such as band-pass filtering. However, the fractional Fourier transform can be 'tuned' to be sensitive to signals of a particular chirp rate (C. Capus et al, IEE Seminar on Time-Scale and Time-Freq. Analysis and Appl., 2000) and can achieve levels of pulse compression similar to those obtained using a matched filter. To this end a system was developed which could generate and transmit linear chirp coded ultrasound signals. The fractional Fourier transform was then used to process the signals received from a simple phantom arrangement. When the transform was used with the optimum transform order corresponding to the chirp rate of the signals, the transform domain signals demonstrated a degree of pulse compression similar to that given by a matched filter. Results are also presented which demonstrate that a chirp signal identified in the fractional Fourier domain may be completely recovered in the time domain through the use of the inverse transform. Matched filtering was found to give a greater degree of pulse compression, but the fraction Fourier method can be applied without a-priori knowledge of the transmitted signal. Further work will be carried out to determine the best way of extracting useful information from the fractional domain signals.

On the orthogonality of anti-leakage Fourier transform based seismic trace interpolation

Abstract: Summary Seismic data regularization, which aims to estimate the seismic traces on a spatially regular grid using the a cquired irregular sampled data, is an interpolation/extrapolation problem. Sampling theory offers the basic conditions for all the seismic data regularization implementations. In sampling theory, Fourier transform plays a crucial role in the analysis of the reconstruction/interpolation basis (interpolant); it estimates the frequency components in frequency/wave-number domain, and its inverse transform creates the seismic data on the desired regular grid. Difficulties arise from the non-orthogonality of the global Fourier basis on an irregular grid, which results in the energy from one frequency component leaks onto others. This well-known phenomenon is called “spectral leakage”. The updated Fourier transform: Anti-leakage Fourier transform (ALFT) offers to overcome the above mentioned difficulties. It estimates the spatial frequency content on a n irregularly sampled grid with significantly reduced frequency leakage. In this paper, we investigate the properties of ALFT and give an insight on how it works. The interpolants are numerically calculated and analyzed in detail. The orthogonality condition of the interpolants is discussed, which demonstrates that the ALFT data reconstruction meets the two most important interpolation conditions (e.g. orthogonal condition and unity condition). With the amplitude analysis on interpolants, the stability of ALFT algorithm is also addressed.

Seismic Data Regularization with Anti-Leakage Fourier Transform

Abstract: D032 Seismic Data Regularization with Anti-leakage Fourier Transform SHENG XU and DON PHAM Abstract 1 Veritas DCG Inc. Town Park Drive Houston Tx 77072 USA In the theory of Fourier reconstruction from discrete seismic data it aims to estimate the spatial frequency content on an irregularly sampled grid. After obtaining the Fourier coefficients the data can be reconstructed on any desired grid. For this type of transform difficulties arise from the non-orthogonality of the global basis functions on an irregular grid. As a consequence energy from one Fourier coefficient leaks onto other coefficients. This well-known phenomenon is called “spectral leakage”.

Iterative approximation environments for modeling the evolution of an image propagating through a physical medium in restoration and other applications

Abstract: Image processing utilizing numerical calculation of fractional exponential powers of a diagonalizable numerical transform operator for use in an iterative or other larger computational environments. In one implementation, a computation involving a similarity transformation is partitioned so that one part remains fixed and may be reused in subsequent iterations. The numerical transform operator may be a discrete Fourier transform operator, discrete fractional Fourier transform operator, centered discrete fractional Fourier transform operator, and other operators, modeling propagation through physical media. Such iterative environments for these types of numerical calculations are useful in correcting the focus of misfocused images which may originate from optical processes involving light (for example, with a lens or lens system) or from particle beams (for example, in electron microscopy or ion lithography).

Speech analysis with the fast chirp transform

Abstract: The Chirp transform is a powerful analysis tool for variable frequency signals such as speech. The computational load represents the main limitation of its original formulation, discouraging its use in real-time applications. This paper analyzes a fast implementation, based on performing time-warping on the signal under analysis, combined with the Fast Fourier Transform. The performance of the Fast Chirp transform depends on the one hand on the estimation of the time-warping operation based on the signal characteristics, and, on the other hand on the interpolation technique used for the warping. Observations from the analysis of speech signals support the method and the further lines.