Showing papers on "Fourier transform published in 2007"
TL;DR: This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies.
Abstract: Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.
2,685 citations
TL;DR: Two algorithms, one based on filtering and the other based on similarity measure, are developed and some applications based on these two algorithms are explored, including strain determination, phase unwrapping, phase-shifter calibration, fault detection, edge detection and fringe segmentation.
620 citations
TL;DR: Hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images, and the properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms.
Abstract: Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed
535 citations
TL;DR: A new class of fractional-order anisotropic diffusion equations for noise removal are introduced which are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function.
Abstract: This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.
440 citations
TL;DR: A more efficient representation is introduced here as a orthogonal set of basis functions that localizes the spectrum and retains the advantageous phase properties of the S-transform, and can perform localized cross spectral analysis to measure phase shifts between each of multiple components of two time series.
363 citations
TL;DR: A Fourier method is proposed for analyzing the stability and convergence of the implicit difference approximation scheme (IDAS), derive the global accuracy of the IDAS, and discuss the solvability.
351 citations
TL;DR: The method described makes use of series reversion, the method of stationary phase, and Fourier transform pairs to derive the two-dimensional point target spectrum for an arbitrary bistatic synthetic aperture radar configuration.
Abstract: This letter derives the two-dimensional point target spectrum for an arbitrary bistatic synthetic aperture radar configuration. The method described makes use of series reversion, the method of stationary phase, and Fourier transform pairs to derive the point target spectrum. The accuracy of the spectrum is controlled by keeping enough terms in the two series expansions, and is verified with a point target simulation
347 citations
TL;DR: The intrinsic time-scale decomposition (ITD) as discussed by the authors decomposes a signal into a sum of proper rotation components, for which instantaneous frequency and amplitude are well defined, and a monotonic trend.
Abstract: We introduce a new algorithm, the intrinsic time-scale decomposition (ITD), for efficient and precise time–frequency–energy (TFE) analysis of signals. The ITD method overcomes many of the limitations of both classical (e.g. Fourier transform or wavelet transform based) and more recent (empirical mode decomposition based) approaches to TFE analysis of signals that are nonlinear and/or non-stationary in nature. The ITD method decomposes a signal into (i) a sum of proper rotation components, for which instantaneous frequency and amplitude are well defined, and (ii) a monotonic trend. The decomposition preserves precise temporal information regarding signal critical points and riding waves, with a temporal resolution equal to the time-scale of extrema occurrence in the input signal. We also demonstrate how the ITD enables application of single-wave analysis and how this, in turn, leads to a powerful new class of real-time signal filters, which extract and utilize the inherent instantaneous amplitude and frequency/phase information in combination with other relevant morphological features.
329 citations
01 Jan 2007
TL;DR: In this paper, the authors classify the Fourier reconstruction methods into three groups: Fourier reconstructions, modified back-projection methods, and iterative direct space methods, where the second group includes convolution back projection as well as weighted back projection.
Abstract: Traditionally, three-dimensional reconstruction methods have been classified into two major groups, Fourier reconstruction methods and direct methods (e.g., Crowther et al., 1970; Gilbert, 1972). Fourier methods are defined as algorithms that restore the Fourier transform of the object from the Fourier transforms of the projections and then obtain the real-space distribution of the object by inverse Fourier transformation. Included in this group are also equivalent reconstruction schemes that use expansions of object and projections into orthogonal function systems (e.g., Cormack, 1963, 1964; Smith et al., 1973; Zeitler, Chapter 4). In contrast, direct methods are defined as those that carry out all calculations in real space. These include the convolution back-projection algorithms (Bracewell and Riddle, 1967; Ramachandran and Lakshminarayanan, 1971; Gilbert, 1972) and iterative algorithms (Gordon et al., 1970; Colsher, 1977). Weighted back-projection methods are difficult to classify in this scheme, since they are equivalent to convolution back-projection algorithms, but work on the real-space data as well as the Fourier transform data of either the object or the projections. Both convolution back-projection and weighted back-projection algorithms are based on the same theory as Fourier reconstruction methods, whereas iterative methods normally do not take into account the Fourier relations between object transform and projection transforms. Thus, it seems justified to classify the reconstruction algorithms into three groups: Fourier reconstruction methods, modified back-projection methods, and iterative direct space methods, where the second group includes convolution backprojection as well as weighted back-projection methods.
276 citations
TL;DR: A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution that can be recovered without cross-talk.
Abstract: A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution. By applying the correct keys which consist of the fractional orders, the random phase masks and the pixel scrambling operator, the two primary images can be recovered without cross-talk. The decryption process is robust against the loss of data. The phase-based image with a larger key space is more sensitive to keys and disturbances than the amplitude-based image. The pixel scrambling operation improves the quality of the decrypted image when noise perturbation occurs. The novel approach is verified by simulations.
240 citations
TL;DR: It is demonstrated that the pseudo-spectral method with the high order Fourier smoothing gives a much better performance than the Pseudo-spectrals with the 2/3 dealiasing rule, and that the error produced by the high orders is highly localized near the region where the solution is most singular.
TL;DR: An alternative method using neural network algorithm has achieved satisfactory results for fast and precise harmonic detection in noisy environments by providing only 1/2 cycle sampled values of distorted waveforms to neural network.
Abstract: Nowadays, harmonic distortion in power systems is attracting significant attention. Traditional technical tools for harmonic distortion analysis using either fast Fourier transform or discrete Fourier transform are, however, susceptible to the presence of noise in the distorted signals. Harmonic detection by using Fourier transformation also requires input data for more than one cycle of the current waveform and requires time for the analysis in the next coming cycle. In this paper, an alternative method using neural network algorithm has achieved satisfactory results for fast and precise harmonic detection in noisy environments by providing only 1/2 cycle sampled values of distorted waveforms to neural network. Sensitivity considerations are conducted to determine the key factors affecting the performance efficiency of the proposed model to reach the lowest errors of testing patterns
TL;DR: This work is to determine whether the HHT allows for empirically-derived characteristics to be used in filter design and application, resulting in better filter performance and enhanced signal-to-noise ratio.
Abstract: Advancements in signal processing may allow for improved imaging and analysis of complex geologic targets found in seismic reflection data. A recent contribution to signal processing is the empirical mode decomposition (EMD) which combines with the Hilbert transform as the Hilbert-Huang transform (HHT). The EMD empirically reduces a time series to several subsignals, each of which is input to the same time-frequency environment via the Hilbert transform. The HHT allows for signals describing stochastic or astochastic processes to be analyzed using instantaneous attributes in the time-frequency domain. The HHT is applied herein to seismic reflection data to: (1) assess the ability of the EMD and HHT to quantify meaningful geologic information in the time and time-frequency domains, and (2) use instantaneous attributes to develop superior filters for improving the signal-to-noise ratio. The objective of this work is to determine whether the HHT allows for empirically-derived characteristics to be used in filter design and application, resulting in better filter performance and enhanced signal-to-noise ratio. Two data sets are used to show successful application of the EMD and HHT to seismic reflection data processing. Nonlinear cable strum is removed from one data set while the other is used to show how the HHT compares to and outperforms Fourier-based processing under certain conditions.
TL;DR: A new and simple way to give mass to the elastic boundary is proposed and it is shown that the method can be applied to many problems for which the boundary mass is important.
Abstract: The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. Most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the method can be applied to many problems for which the boundary mass is important. The method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. Two verifications of the method are given. One is a numerical convergence study that shows that our numerical scheme is second-order accurate for a particular test problem. The other is direct comparison with experimental data of vortex-induced vibrations of a massive cylinder, which shows that the results obtained by the present method are quite comparable to the experimental data.
TL;DR: An image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders is presented, independent of additional random phases as the encryption/ decryption keys.
TL;DR: In this article, a system and algorithm to achieve full range complex Fourier domain optical coherence tomography (OCT) capable of imaging biological tissues in vivo was presented, which utilizes the Hilbert transformation to obtain the analytic functions for spatial interference signals obtained from each single wavelength covered in the broadband OCT light source before performing the Fourier transformation to localize the scatters within a sample.
Abstract: The author presents a system and algorithm to achieve full range complex Fourier domain optical coherence tomography (OCT) capable of imaging biological tissues in vivo. The method utilizes the Hilbert transformation to obtain the analytic functions for spatial interference signals obtained from each single wavelength covered in the broadband OCT light source before performing the Fourier transformation to localize the scatters within a sample. A constant carrier frequency is introduced in the spatial OCT interference signal so that its Hilbert transformation is strictly equal to its quadrature representation. The method is experimentally validated for in vivo imaging.
TL;DR: The main properties of the gyrator operation which produces a rotation in the twisting phase planes are formulated and this transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information.
Abstract: In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position - spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information.As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.
TL;DR: To demonstrate the ability of this method to capture molecular dynamics, couplings and structure found in the conventional boxcar 2D FT spectroscopy, a series of 2D spectra of a metal carbonyl, and a beta-sheet protein are acquired.
Abstract: Two-dimensional (2D) Fourier transform (FT) infrared spectroscopy is performed by using a collinear pulse-pair pump and probe geometry with conventional optics. Simultaneous collection of the third-order response and pulse-pair timing permit automated phasing and rapid acquisition of 2D absorptive spectra. To demonstrate the ability of this method to capture molecular dynamics, couplings and structure found in the conventional boxcar 2D FT spectroscopy, a series of 2D spectra of a metal carbonyl, and a beta-sheet protein are acquired.
TL;DR: In this article, the Fourier localization technique and Bony's para-product decomposition were used to improve the regularity criterion of weak solution for 3D viscous magneto-hydrodynamics equations.
Abstract: We improve and extend some known regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations by means of the Fourier localization technique and Bony's para-product decomposition.
TL;DR: In this article, a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly's evolutionary spectral representation theory is presented.
Abstract: This paper presents a rigorous derivation of a previously known formula for simulation of one-dimensional, univariate, nonstationary stochastic processes integrating Priestly's evolutionary spectral representation theory. Applying this formula, sample functions can be generated with great computational efficiency. The simulated stochastic process is asymptotically Gaussian as the number of terms tends to infinity. This paper shows that (1) these sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic process when the number of terms in the cosine series is large, i.e., the ensemble averaged evolutionary power spectral density function (PSDF) or autocorrelation function approaches the corresponding target function as the sample size increases, and (2) the simulation formula, under certain conditions, can be reduced to that for nonstationary white noise process or Shinozuka's spectral representation of stationary process. In addition to derivation of simulation formula, three methods are developed in this paper to estimate the evolutionary PSDF of a given time-history data by means of the short-time Fourier transform (STFT), the wavelet transform (WT), and the Hilbert-Huang transform (HHT). A comparison of the PSDF of the well-known El Centro earthquake record estimated by these methods shows that the STFT and the WT give similar results, whereas the HHT gives more concentrated energy at certain frequencies. Effectiveness of the proposed simulation formula for nonstationary sample functions is demonstrated by simulating time histories from the estimated evolutionary PSDFs. Mean acceleration spectrum obtained by averaging the spectra of generated time histories are then presented and compared with the target spectrum to demonstrate the usefulness of this method.
TL;DR: In this paper, the quaternionic Fourier transform (QFT) is applied to quaternion fields and properties useful for applications are investigated, and different forms of the QFT lead to different Plancherel theorems.
Abstract: We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.
14 Mar 2007
TL;DR: This study shows that among all these methods, the Fourier transform inversion technique is the most powerful but also the most computationally expensive.
TL;DR: In this article, the point symmetry of the crystal lattice sums of integrals involving fitting functions is identified and eliminated through the use of Poisson transformed fitting functions and of dipole-corrected product distributions.
Abstract: When solving the M\o{}ller-Plesset second order perturbation theory (MP2) equations for periodic systems using a local-correlation approach [J. Chem. Phys. 122 (2005) 094113], the computational bottleneck is represented by the evaluation of the two-electron Coulomb interaction integrals between product distributions, each involving a Wannier function and a projected atomic orbital. While for distant product distributions a multipolar approximation performs very efficiently, the four index transformation for close-by distributions, which by far constitutes the bottleneck of correlated electronic structure calculations of crystals, can be avoided through the use of density fitting techniques. An adaptation of that scheme to translationally periodic systems is described, based on Fourier transformation techniques. The formulas and algorithms adopted allow the point symmetry of the crystal to be exploited. Problems related to the possible divergency of lattice sums of integrals involving fitting functions are identified and eliminated through the use of Poisson transformed fitting functions and of dipole-corrected product distributions. The iterative scheme for solving the linear local MP2 (LMP2) equations is revisited. Prescreening in the evaluation of the residual matrix is introduced, which significantly lowers the scaling of the LMP2 equations.
TL;DR: It is shown that increasing the number of crossband filters not necessarily implies a lower steady-state mean-square error (mse) in subbands, and analytical relations between the number and length of the input signal are derived.
Abstract: In this paper, we investigate the influence of crossband filters on a system identifier implemented in the short-time Fourier transform (STFT) domain. We derive analytical relations between the number of crossband filters, which are useful for system identification in the STFT domain, and the power and length of the input signal. We show that increasing the number of crossband filters not necessarily implies a lower steady-state mean-square error (mse) in subbands. The number of useful crossband filters depends on the power ratio between the input signal and the additive noise signal. Furthermore, it depends on the effective length of input signal employed for system identification, which is restricted to enable tracking capability of the algorithm during time variations in the system. As the power of input signal increases or as the time variations in the system become slower, a larger number of crossband filters may be utilized. The proposed subband approach is compared to the conventional fullband approach and to the commonly used subband approach that relies on multiplicative transfer function (MTF) approximation. The comparison is carried out in terms of mse performance and computational complexity. Experimental results verify the theoretical derivations and demonstrate the relations between the number of useful crossband filters and the power and length of the input signal
TL;DR: In this paper, a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same system was proposed, and the freezing parameters of the system were analyzed analytically.
Abstract: We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.
TL;DR: This research overcomes the limitations on sampling imposed by Fourier-based algorithms by the development of a fast shifted Fresnel transform, which is used to develop a tiling approach to hologram construction and reconstruction.
Abstract: Fourier-based approaches to calculate the Fresnel diffraction of light provide one of the most efficient algorithms for holographic computations because this permits the use of the fast Fourier transform (FFT). This research overcomes the limitations on sampling imposed by Fourier-based algorithms by the development of a fast shifted Fresnel transform. This fast shifted Fresnel transform is used to develop a tiling approach to hologram construction and reconstruction, which computes the Fresnel propagation of light between parallel planes having different resolutions.
TL;DR: A new algorithm is developed for the phase retrieval problem that exploits a signal's compressibility rather than its support to recover it from Fourier transform magnitude measurements.
Abstract: The theory of compressive sensing enables accurate and robust signal reconstruction from a number of measurements
dictated by the signal's structure rather than its Fourier bandwidth. A key element of the theory is
the role played by randomization. In particular, signals that are compressible in the time or space domain can
be recovered from just a few randomly chosen Fourier coefficients. However, in some scenarios we can only observe
the magnitude of the Fourier coefficients and not their phase. In this paper, we study the magnitude-only
compressive sensing problem and in parallel with the existing theory derive sufficient conditions for accurate
recovery. We also propose a new iterative recovery algorithm and study its performance. In the process, we
develop a new algorithm for the phase retrieval problem that exploits a signal's compressibility rather than its
support to recover it from Fourier transform magnitude measurements.
TL;DR: In this article, a low-sidelobe pattern synthesis method for planar array antennas with periodic element spacing is described, where the array factor is related to the element excitations through an inverse Fourier transform.
Abstract: A new and very fast low-sidelobe pattern synthesis method for planar array antennas with periodic element spacing is described. The basic idea of the method is that since the array factor is related to the element excitations through an inverse Fourier transform, the element excitations can be derived from the array factor through a direct Fourier transform. Starting with an initial set of suitable element excitations the array factor is calculated. After matching the array factor to the prescribed pattern, an updated set of excitations is obtained through a direct Fourier transform performed on the matched array factor. From this updated set, only the samples associated with the aperture are retained, where after a new array factor is calculated. The whole process is repeated until the updated array factor does not violate any longer the pattern requirements. The proposed synthesis method provides significant improvements in terms of performance, computational speed, flexibility, and ease of implementation in software to the methods described in reviewed literature. A number of representative examples are presented to demonstrate the various unique capabilities of the method. The results include sum and difference patterns for circular and elliptical aperture shapes featuring uniform ultra low sidelobes
TL;DR: In this paper, the generalized fractional Schrodinger equation with space and time fractional derivatives is constructed and solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function.
Abstract: In this paper the generalized fractional Schrodinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schrodinger equation and the ones in standard quantum.