Showing papers on "Fast Fourier transform published in 2002"
TL;DR: A simplified scoring system is proposed that performs well for reducing CPU time and increasing the accuracy of alignments even for sequences having large insertions or extensions as well as distantly related sequences of similar length.
Abstract: A multiple sequence alignment program, MAFFT, has been developed. The CPU time is drastically reduced as compared with existing methods. MAFFT includes two novel techniques. (i) Homologous regions are rapidly identified by the fast Fourier transform (FFT), in which an amino acid sequence is converted to a sequence composed of volume and polarity values of each amino acid residue. (ii) We propose a simplified scoring system that performs well for reducing CPU time and increasing the accuracy of alignments even for sequences having large insertions or extensions as well as distantly related sequences of similar length. Two different heuristics, the progressive method (FFT-NS-2) and the iterative refinement method (FFT-NS-i), are implemented in MAFFT. The performances of FFT-NS-2 and FFT-NS-i were compared with other methods by computer simulations and benchmark tests; the CPU time of FFT-NS-2 is drastically reduced as compared with CLUSTALW with comparable accuracy. FFT-NS-i is over 100 times faster than T-COFFEE, when the number of input sequences exceeds 60, without sacrificing the accuracy.
12,003 citations
TL;DR: In this article, the authors present a summary of the monitoring methods, signal analysis and diagnostic techniques for tool wear and failure monitoring in drilling that have been tested and reported in the literature.
Abstract: This paper presents a summary of the monitoring methods, signal analysis and diagnostic techniques for tool wear and failure monitoring in drilling that have been tested and reported in the literature. The paper covers only indirect monitoring methods such as force, vibration and current measurements, i.e. direct monitoring methods based on dimensional measurement etc. are not included. Signal analysis techniques cover all the methods that have been used with indirect measurements including e.g. statistical parameters and Fast Fourier and Wavelet Transform. Only a limited number of automatic diagnostic tools have been developed for diagnosis of the condition of the tool in drilling. All of these rather diverse approaches that have been available are covered in this study. In the reported material there are both success stories and also those that have not been so successful. Only in a few of the papers have attempts been made to compare the chosen approach with other methods. Many of the papers only present one approach and unfortunately quite often the test material of the study is limited especially in what comes to the cutting process parameter variation, i.e. variation of cutting speed, feed rate, drill diameter and material and also workpiece material.
309 citations
TL;DR: In this article, the DC-FFT algorithm was used to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy, and a set of general formulas of the frequency response function for the elastic field was derived and verified.
Abstract: The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.
265 citations
01 Jan 2002
TL;DR: This report tries to give a practical overview about the estimation of power spectra/power spectral densities using the DFT/FFT and includes a detailed list of common and useful window functions, among them the often neglected flat-top windows.
Abstract: This report tries to give a practical overview about the estimation of power spectra/power spectral densities using the DFT/FFT. One point that is emphasized is the relationship between estimates of power spectra and power spectral densities which is given by the effective noise bandwidth (ENBW). Included is a detailed list of common and useful window functions, among them the often neglected flat-top windows. Special highlights are a procedure to test new programs, a table of comprehensive graphs for each window and the introduction of a whole family of new flat-top windows that feature sidelobe suppression levels of up to −248dB, as compared with −90dB of the best flat-top windows available until now.
262 citations
01 Jan 2002
TL;DR: In this article, the authors investigated a method for pricing the generic spread option beyond the classical two-factor Black-Scholes framework by extending the fast Fourier Transform technique introduced by Carr & Madan (1999) to a multi-factor setting.
Abstract: We investigate a method for pricing the generic spread option beyond the classical two-factor Black-Scholes framework by extending the fast Fourier Transform technique introduced by Carr & Madan (1999) to a multi-factor setting The method is applicable to models in which the joint characteristic function of the prices of the underlying assets forming the spread is known analytically This enables us to incorporate stochasticity in the volatility and correlation structure — a focus of concern for energy option traders — by introducing additional factors within an affine jump-diffusion framework Furthermore, computational time does not increase significantly as additional random factors are introduced, since the fast Fourier Transform remains two dimensional in terms of the two prices defining the spread This yields considerable advantage over Monte Carlo and PDE methods and numerical results are presented to this effect
166 citations
TL;DR: A novel symmetrization method for solving the transport of intensity equation (TIE) using fast Fourier transforms for situations where the input images may or may not exhibit spatial periodicity.
152 citations
Book•
15 Jan 2002
TL;DR: This chapter discusses characterization of Signals, use of Higher-Order Spectra in Signal Processing, and nonparametric methods for Power Spectrum Estimation.
Abstract: 1. Introduction. Characterization of Signals. Characterization of Linear Time-Invariant Systems. Sampling of Signals. Linear Filtering Methods Based on the DFT. The Cepstrum. Summary and References. Problems. 2. Algorithms for Convolution and DFT. Modulo Polynomials. Circular Convolution as Polynomial Multiplication mod un- 1. A Continued Fraction of Polynomials. Chinese Remainder Theorem for Polynomials. Algorithms for Short Circular Convolutions. How We Count Multiplications. Cyclotomic Polynomials. Elementary Number Theory. Convolution Length and Dimension. The DFT as a Circular Convolution. Winograd's DFT Algorithm. Number-Theoretic Analogy of DFT. Number-Theoretic Transform. Split-Radix FFT. Autogen Technique. Summary and References. Problems. 3. Linear Prediction and Optimum Linear Filters. Innovations Representation of a Stationary Random Process. Forward and Backward Linear Prediction. Solution of the Normal Equations. Properties of the Linear Prediction-Error Filters. AR Lattice and ARMA Lattice-Ladder Filters. Wiener Filters for Filtering and Prediction. Summary and References. Problems. 4. Least-Squares Methods for System Modeling and Filter Design. System Modeling and Identification. Lease-Squares Filter Design for Prediction and Deconvolution. Solution of Least-Squares Estimation Problems. Summary and References. Problems. 5. Adaptive Filters. Applications of Adaptive Filters. Adaptive Direct-Form FIR Filters. Adaptive Lattice-Ladder Filters. Summary and References. Problems. 6. Recursive Least-Squares Algorithms for Array Signal Processing. QR Decomposition for Least-Squares Estimation. Gram-Schmidt Orthogonalization for Least-Squares Estimation. Givens Algorithm for Time-Recursive Least-Squares Estimation. Recursive Least-Squares Estimation Based on the Householder Transformation. Order-Recursive Least-Squares Estimation Algorithms. Summary and References. Problems. 7. QRD-Based Fast Adaptive Filter Algorithms. Background. QRD Lattice. Multichannel Lattice. Fast QR Algorithm. Multichannel Fast QR Algorithm. Summary and References. Problems. 8. Power Spectrum Estimation. Estimation of Spectra from Finite-Duration Observations of Signals. Nonparametric Methods for Power Spectrum Estimation. Parametric Methods for Power Spectrum Estimation. Minimum-Variance Spectral Estimation. Eigenanalysis Algorithms for Spectrum Estimation. Summary and References. Problems. 9. Signal Analysis with Higher-Order Spectra. Use of Higher-Order Spectra in Signal Processing. Definition and Properties of Higher-Order Spectra. Conventional Estimators for Higher-Order Spectra. Parametric Methods for Higher-Order Spectrum Estimation. Cepstra of Higher-Order Spectra. Phase and Magnitude Retrieval from the Bispectrum. Summary and References. Problems. References. Index.
152 citations
TL;DR: In this article, an efficient technique is developed to recognize target type using one-dimensional range profiles using MCS algorithm. But the proposed technique utilizes the multiple signal classification algorithm to generate superresolved range profiles.
Abstract: An efficient technique is developed to recognize target type using one-dimensional range profiles. The proposed technique utilizes the Multiple Signal Classification algorithm to generate superresolved range profiles. Their central moments are calculated to provide translation-invariant and level-invariant feature vectors. Next, the computed central moments are mapped into values between zero and unity, followed by a principal component analysis to eliminate the redundancy of feature vectors. The obtained features are classified based on the Bayes classifier, which is one of the statistical classifiers. Recognition results using five different aircraft models measured at compact range are presented to assess the effectiveness of the proposed technique, and they are compared with those of the conventional range profiles obtained by inverse fast Fourier transform.
152 citations
16 Nov 2002
TL;DR: The high-resolution direct numerical simulations of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator, based on the Fourier spectral method, and yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.
Abstract: The high-resolution direct numerical simulations (DNSs) of incompressible turbulence with numbers of grid points up to 40963 have been executed on the Earth Simulator (ES). The DNSs are based on the Fourier spectral method, so that the equation for mass conservation is accurately solved. In DNS based on the spectral method, most of the computation time is consumed in calculating the three-dimensional (3D) Fast Fourier Transform (FFT), which requires huge-scale global data transfer and has been the major stumbling block that has prevented truly high-performance computing. By implementing new methods to efficiently perform the 3D-FFT on the ES, we have achieved DNS at 16.4 Tflops on 20483 grid points. The DNS yields an energy spectrum exhibiting a wide inertial subrange, in contrast to previous DNSs with lower resolutions, and therefore provides valuable data for the study of the universal features of turbulence at large Reynolds number.
145 citations
TL;DR: It is shown that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki’s method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schrodinger equation with time-dependent potentials.
Abstract: We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki’s method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schrodinger equation with time-dependent potentials. When applied to the Walker–Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest–Ruth algorithm using the same number of fast Fourier transforms. Compared to the second order split-operator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a one-parameter family of algorithms, and that the parameter can be further optimized for specific applications.
139 citations
10 Dec 2002
TL;DR: This work presents a fast back-projection algorithm for bistatic SAR imaging, motivated by a fastBack- projection algorithm previously proposed for tomography, which has a reduced computational cost, on the same order as that of direct Fourier reconstruction.
Abstract: Using a far-field model, bistatic synthetic aperture radar (SAR) acquires Fourier data on a rather unusual, non-Cartesian grid in the Fourier domain. Previous image formation algorithms were mainly based on direct Fourier reconstruction to take advantage of the FFT, but the irregular coverage of the available Fourier domain data and the 2-D interpolation in the Fourier domain may adversely affect the accuracy of image reconstruction. Back-projection techniques avoid Fourier-domain interpolation, but ordinarily have huge computational cost. We present a fast back-projection algorithm for bistatic SAR imaging, motivated by a fast back-projection algorithm previously proposed for tomography. It has a reduced computational cost, on the same order as that of direct Fourier reconstruction. Furthermore, this approach can be used for near-field imaging. Simulation results verify the performance of this new algorithm.
TL;DR: An iterative reconstruction framework for diffraction ultrasound tomography that makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion and incorporation of total variation regularization is shown.
Abstract: We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broad-band illumination allows significant reduction of the number of projections compared to straight ray tomography. The proposed algorithm makes use of forward nonuniform fast Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows the reduction of noise and Gibbs phenomena while preserving the edges. The complexity of the NUFFT-based reconstruction is comparable to the frequency-domain interpolation (gridding) algorithm, whereas the reconstruction accuracy (in sense of the L/sup 2/ and the L/sup /spl infin// norm) is better.
TL;DR: Multiwavelength recording and reconstruction of a three-dimensional object are realized by use of phase-shifting digital holography, in which a phase shift is introduced with an achromatic phase shift based on the geometric phase.
Abstract: Multiwavelength recording and reconstruction of a three-dimensional object are realized by use of phase-shifting digital holography. Red, green, and blue lines emitted from a white-light He-Cd laser are used for one-step recording of the complex amplitude of the object with a color CCD camera, in which a phase shift is introduced with an achromatic phase shifter based on the geometric phase. Three color images are reconstructed and successfully combined in a computer by use of Fresnel transformation based on a convolution.
TL;DR: A reduced complexity channel estimation for OFDM systems with transmit diversity is proposed by exploiting the correlation of the adjacent subchannel responses to achieve a substantial performance improvement over the existing method without any added complexity.
Abstract: A reduced complexity channel estimation for OFDM systems with transmit diversity is proposed by exploiting the correlation of the adjacent subchannel responses. The sizes of the matrix inverse and the FFTs required in the channel estimation at every OFDM data symbol are reduced by half of the existing method for OFDM systems with nonconstant modulus subcarrier symbols or constant modulus subcarrier symbols with some guard tones. The complexity reduction of half FFTs size and some matrix multiplications is still achieved for constant modulus subcarrier symbols with no guard tones. The price for the complexity reduction is a slight BER degradation and for the channels with small relative delay spreads, the BER performance of the reduced complexity method becomes quite comparable to the existing method. An alternative approach for the number of significant taps required in the channel estimation is described which achieves a comparable performance to the case with the known suitable number of significant taps. A simple modification which reduces the lost leakage of the nonsample-spaced channel paths is also proposed. This modification achieves a substantial performance improvement over the existing method without any added complexity.
07 Nov 2002
TL;DR: This work proposes a novel feature vector suitable for searching collections of 3D-object images by shape similarity by applying the fast Fourier transform on the sphere and obtaining Fourier coefficients for spherical harmonics.
Abstract: We propose a novel feature vector suitable for searching collections of 3D-object images by shape similarity. In this search, a polygonal mesh model serves as a query. For each model, feature vectors are automatically extracted and stored. Shape similarity between 3D-objects in the search space is determined by finding and ranking nearest neighbors in the feature vector space. Ranked objects are retrieved for inspection, selection, and processing. The feature vector is obtained by forming a complex function on the sphere. Afterwards, we apply the fast Fourier transform (FFT) on the sphere and obtain Fourier coefficients for spherical harmonics. The absolute values of the coefficients form the feature vector. Retrieval efficiency of the new approach is evaluated by constructing precision/recall diagrams and using two different 3D-model databases. We compared the approach with two methods based on real functions on the sphere. Our empirical comparison showed that the complex feature vector performed best. We also prepared a Web-based retrieval system for testing the methods discussed.
TL;DR: In this article, a diffraction tomographic (DT) algorithm has been proposed for detecting 3D dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy.
Abstract: A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm.
TL;DR: This work compares the performance in terms of accuracy and efficiency of four algorithms: the classical SVD algorithm based on the QR decomposition, the Lanczos algorithm, the Lancaster algorithm with partial reorthogonalization, and the implicitly restarted Lanczos algorithms.
TL;DR: In this paper, the authors show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schroedinger equation with time-dependent potentials.
Abstract: We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schroedinger equation with time-dependent potentials. When applied to the Walker-Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest-Ruth algorithm using the same number of Fast Fourier Transforms. When compared to the second order split-operator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a one-parameter family of algorithms, and that the parameter can be further optimized for specific applications.
10 Dec 2002
TL;DR: Simulations show that for fast time-varying channels, optimized BFDM systems can outperform conventional OFDM systems with respect to ISI/ICI and two methods for an ISI-minimizing pulse design are proposed.
Abstract: This paper considers practically relevant aspects and advantages of pulse-shaping orthogonal/biorthogonal frequency division multiplexing (OFDM/BFDM) systems. We analyze the intersymbol/intercarrier interference (ISI/ICI) in such systems when they operate over time-varying channels. Two methods for an ISI/ICI-minimizing pulse design are proposed, and efficient FFT-based modulator and demodulator implementations are presented. Simulations show that for fast time-varying channels, optimized BFDM systems can outperform conventional OFDM systems with respect to ISI/ICI.
01 Sep 2002
TL;DR: A survey of the numerous analysis methods proposed in order to extract the frequency, amplitude, and phase of sinusoidal components from stationary sounds, which is of great interest for spectral modeling, digital audio effects, or pitch tracking for instance.
Abstract: This paper makes a survey of the numerous analysis methods proposed in order to extract the frequency, amplitude, and phase of sinusoidal components from stationary sounds, which is of great interest for spectral modeling, digital audio effects, or pitch tracking for instance. We consider different methods that improve the frequency resolution of a plain FFT. We compare the accuracies in frequency and amplitude of all these methods. As the results show, all considered methods have a great advantage over the plain FFT.
TL;DR: In this paper, a real-time kinematic (RTK) global positioning system (GPS) has been developed and installed on the Humen bridge for on-line monitoring of bridge deck movements.
01 Jan 2002
TL;DR: This report gives a detailed presentation of the implementation of a new fast algorithm for image segmentation based upon Mumford-Shah functionals, which has computational complexity on the order of the Fast Fourier Transform, the benchmark for fast algorithms.
Abstract: : This report gives a detailed presentation of the implementation of a new fast algorithm for image segmentation. The original motivation for development of the algorithm was the segmentation of synthetic aperture radar (SAR) imagery into homogeneous regions for target detection in the Analysts' Detection Support System. However, the algorithm is a general one based upon Mumford-Shah functionals, and there is no technical reason why it could not also be used for other imaging modalities, including multiband imagery. The algorithm has computational complexity on the order of the Fast Fourier Transform, the benchmark for fast algorithms.
TL;DR: This paper deals with the choice of the apodization function to be applied to the complex visibilities of the SMOS mission, and describes how discrete Fourier transform calculations over hexagonal grids can be performed using a simple algorithm.
Abstract: It is now well established that synthetic aperture imaging radiometers promise to be powerful sensors for high-resolution observations of the Earth at low microwave frequencies. Within this context, the European Space Agency is currently developing the Soil Moisture and Ocean Salinity (SMOS) mission. The Y-shaped array selected for SMOS is fitted with equally spaced antennae and leads to a natural hexagonal sampling of the Fourier plane. This paper deals with the choice of the apodization function to be applied to the complex visibilities. The aim of this function is to reduce the Gibbs phenomenon produced by the finite extent of the star-shaped frequency coverage and the resulting sharp frequency cut-off. A large number of windows are introduced. A comparison of these in terms of their spatial domain properties is given, according to criteria relevant for remote sensing of the Earth's surface. This paper also describes how discrete Fourier transform calculations over hexagonal grids can be performed using a simple algorithm. Actually, standard fast Fourier transform algorithms designed for Cartesian grids and which have a long track record of optimization can be reused. Finally, an interpolation formula is given for resampling data from hexagonal grids without introducing any aliasing artifacts in the resampled data.
TL;DR: The use of the fast Fourier transform (FFT) test to measure the integral nonlinearity (INL) of analog-to-digital (A/D) converters is examined and it appears to be very convenient when the device under test has high resolution and a smoothed approximation of the INL is sufficient.
Abstract: In this paper, the use of the fast Fourier transform (FFT) test to measure the integral nonlinearity (INL) of analog-to-digital (A/D) converters is examined. The derived INL is a linear combination of Chebyshev polynomials, where the coefficients are the spurious harmonics of the output spectrum. The accuracy of the test is examined theoretically, in simulations and in practical devices, particularly for the critical (and typical) case when sudden jumps are present in the actual INL. The examined methodology appears to be very convenient when the device under test has high resolution (16-20 bits) and a smoothed approximation of the INL is sufficient, as the FFT test is in this case thousands of times faster than the customary histogram test and static nonlinearity test.
TL;DR: In this article, the authors evaluated the statistical variance in the once-per-revolution sampled audio signal during milling as a chatter indicator and showed that, due to the synchronous and asynchronous nature of stable and unstable cuts, respectively, once per-revolution sampling leads to a tight distribution of values for stable cuts, with a corresponding low variance, and a wider sample distribution for unstable cuts with an associated high variance.
Abstract: The purpose of this study is an evaluation of the statistical variance in the once-per-revolution sampled audio signal during milling as a chatter indicator. It is shown that, due to the synchronous and asynchronous nature of stable and unstable cuts, respectively, once-per-revolution sampling leads to a tight distribution of values for stable cuts, with a corresponding low variance, and a wider sample distribution for unstable cuts, with an associated high variance. A comparison of stability maps developed using: 1) analytic techniques, and 2) the variance from once-per-revolution sampled time-domain simulations is provided and good agreement is shown. Experimental agreement between the well-known Fast Fourier Transform (FFT) chatter detection method, that analyzes the content of the FFT spectrum for chatter frequencies, and the new variance-based technique is also demonstrated.
TL;DR: The implementation is consistent with the equations of fluid flow and produces velocity fields that contain incompressible rotational structures and dynamically react to user-supplied forces.
Abstract: This paper presents a very simple implementation of a fluid solver. The implementation is consistent with the equations of fluid flow and produces velocity fields that contain incompressible rotational structures and dynamically react to user-supplied forces. Specialized for a fluid which wraps around in space, it allows us to take advantage of the Fourier transform, which greatly simplifies many aspects of the solver. Indeed, given a Fast Fourier Transform, our solver can be implemented in roughly one page of readable C code. The solver is a good starting point for anyone interested in coding a basic fluid solver. The fluid solver presented is useful also as a basic motion primitive that can be used for many different applications in computer graphics.
TL;DR: This paper presents a new Fourier‐based sampling scheme and sliding window reconstruction that facilitates fast scanning without needing correction or interpolation and can be used on virtually any MR scanner since it requires no specialized hardware.
Abstract: Applications of dynamic contrast enhanced MR imaging are increasing and require both high spatial resolution and high temporal resolution. Perfusion studies using susceptibility contrast in particular require very high temporal resolution. The sliding window reconstruction is a technique for increasing temporal resolution. It has previously been applied to radial and spiral sampling, but these schemes require extensive correction and interpolation during image reconstruction. Fourier raw data can be reconstructed simply and quickly using the fast fourier transform (FFT). This paper presents a new Fourier-based sampling scheme and sliding window reconstruction that facilitates fast scanning without needing correction or interpolation. This technique can be used on virtually any MR scanner since it requires no specialized hardware. It is implemented here as a dual gradient echo sequence providing simultaneous T1- and T2*-weighted images with a time resolution of 1.1 s. Copyright © 2002 John Wiley & Sons, Ltd.
TL;DR: A simple alternative procedure to reduce leakage in the Fourier spectrum of a periodic signal is proposed and results obtained are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.
Abstract: The Fourier spectrum of a periodic signal may be obtained by fast Fourier transform algorithms, but, as is well known, special care must be taken to avoid severe distortions introduced by the sampling process. The main problem is the leakage generated by the truncation required to obtain a finite length sampled data. The usual procedure to reduce leakage is to multiply the sampled signal by a weighting window. Several kinds of windows have been proposed in the literature, and today they are also included in many commercial instruments. A simple alternative procedure is proposed in this paper. It is implemented with a PC compatible data acquisition board (DAQ) and consists of an algorithm that uses decimation and interpolation techniques. This algorithm is equivalent to the use of an adjustable sampling frequency and correspondingly an adjustable window size. Results obtained by this method on both harmonic and polyharmonic signals are empirically analyzed and compared with those given by an instrument with built-in FFT capabilities.
TL;DR: It is shown that a single thermally-modulated tin oxide-based resistive microsensor can discriminate between two different pollutant gases (CO and NO2) and their mixtures.
Abstract: It is shown that a single thermally-modulated tin oxide based resistive microsensor can discriminate between two different pollutant gases (CO and NO2) and their mixtures. The method employs a novel feature-extraction and pattern classification method, which is based on a 1-D discrete Wavelet transform and a Fuzzy ARTMAP neural network. The wavelet technique is more effective than FFT in terms of both data compression and drift rejection. Furthermore, Fuzzy ARTMAP networks lead to a 100% success rate in gas recognition in just 2 training epochs, which is significantly lower than the number of epochs required to train the back-propagation network.
TL;DR: The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.
Abstract: An algorithm for the estimation of the frequency of a complex sinusoid in noise is proposed. The estimator consists of multiple applications of lowpass filtering and decimation, frequency estimation by linear prediction, and digital heterodyning. The estimator has a significantly reduced threshold relative to existing phase-based algorithms and performance close to that of maximum likelihood estimation. In addition, the mean-squared error performance is within 0.7 dB of the Cramer-Rao bound (CRB) at signal-to-noise ratios (SNRs) above threshold. Unlike many autocorrelation and phase-based methods, the proposed algorithm's performance is uniform across a frequency range of -/spl pi/ to /spl pi/. The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.