Showing papers on "Fast Fourier transform published in 2004"

Accelerating the Nonuniform Fast Fourier Transform

Abstract: The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain. When the sampling is uniform, the fast Fourier transform (FFT) allows this calculation to be computed in O(N log N ) operations rather than O(N 2 ) operations. Unfortunately, when the sampling is nonuniform, the FFT does not apply. Over the last few years, a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform FFTs (NUFFTs). These rely on a mixture of interpolation and the judicious use of the FFT on an oversampled grid (A. Dutt and V. Rokhlin, SIAM J. Sci. Comput., 14 (1993), pp. 1368-1383). In this paper, we observe that one of the standard interpolation or "gridding" schemes, based on Gaussians, can be accelerated by a significant factor without precomputation and storage of the interpolation weights. This is of particular value in two- and three- dimensional settings, saving either 10 d N in storage in d dimensions or a factor of about 5-10 in CPUtime (independent of dimension).

Option Pricing by Transform Methods: Extensions, Unification, and Error Control

Abstract: We extend and unify Fourier-analytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.

Minimum weighted norm interpolation of seismic records

Abstract: In seismic data processing, we often need to interpolate and extrapolate data at missing spatial locations. The reconstruction problem can be posed as an inverse problem where, from inadequate and incomplete data, we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired.We propose a wavefield reconstruction scheme for spatially band‐limited signals. The method entails solving an inverse problem where a wavenumber‐domain regularization term is included. The regularization term constrains the solution to be spatially band‐limited and imposes a prior spectral shape. The numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix–vector multiplications, implemented via the fast Fourier transform (FFT), is adopted. The algorithm can be used to perform multidimensional reconstruction in any spatial domain.

Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields

Abstract: The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized method is given. The advantages and the disadvantages of the method with respect to other typical methods are discussed.

Parallel Scientific Computation: A Structured Approach using BSP and MPI

Abstract: 1. Introduction 2. LU decomposition 3. The fast Fourier transform 4. Sparse matrix-vector multiplication A. Auxiliary BSPedupack functions B. A quick reference guide to BSPlib C. Programming in BSP style using MPI References Index

Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Algorithms

Abstract: SPIRAL is a generator for libraries of fast software implementations of linear signal processing transforms. These libraries are adapted to the computing platform and can be re-optimized as the hardware is upgraded or replaced. This paper describes the main components of SPIRAL: the mathematical framework that concisely describes signal transforms and their fast algorithms; the formula generator that captures at the algorithmic level the degrees of freedom in expressing a particular signal processing transform; the formula translator that encapsulates the compilation degrees of freedom when translating a specific algorithm into an actual code implementation; and, finally, an intelligent search engine that finds within the large space of alternative formulas and implementations the "best" match to the given computing platform. We present empirical data that demonstrate the high performance of SPIRAL generated code.

Reliable low-power digital signal processing via reduced precision redundancy

Abstract: In this paper, we present a novel algorithmic noise-tolerance (ANT) technique referred to as reduced precision redundancy (RPR). RPR requires a reduced precision replica whose output can be employed as the corrected output in case the original system computes erroneously. When combined with voltage overscaling (VOS), the resulting soft digital signal processing system achieves up to 60% and 44% energy savings with no loss in the signal-to-noise ratio (SNR) for receive filtering in a QPSK system and the butterfly of fast Fourier transform (FFT) in a WLAN OFDM system, respectively. These energy savings are with respect to optimally scaled (i.e., the supply voltage equals the critical voltage V/sub dd-crit/) present day systems. Further, we show that the RPR technique is able to maintain the output SNR for error rates of up to 0.09/sample and 0.06/sample in an finite impulse response filter and a FFT block, respectively.

Wavelet deconvolution in a periodic setting

Abstract: In this paper, we present an inverse estimation procedure which combines Fourier analysis with wavelet expansion. In the periodic setting, our method can recover a blurred function observed in white noise. The blurring process is achieved through a convolution operator which can either be smooth (polynomial decay of the Fourier transform) or irregular (such as the convolution with a box-car). The proposal is non-linear and does not require any prior knowledge of the smoothness class; it enjoys fast computation and is spatially adaptive. This contrasts with more traditional ltering methods which demand a certain amount of regularisation and often fail to recover non-homogeneous functions. A ne tuning of our method is derived via asymptotic minimax theory which reveals some key dierences with the direct case of Donoho et al. (1995): (a) band-limited wavelet families have nice theoretical and computing features; (b) the high frequency cut o depends on the spectral characteristics of the convolution kernel; (c) thresholds are level dependent in a geometric fashion. We tested our method using simulated lidar data for underwater remote sensing. Both visual and numerical results show an improvement over existing methods. Finally, the theory behind our estimation paradigm gives a complete characterisation of the ’Maxiset’ of the method i.e. the set of functions where the method attains a near-optimal rate of convergence for a variety of L p loss functions.

A 64-point Fourier transform chip for high-speed wireless LAN application using OFDM

Abstract: In this paper, we present a novel fixed-point 16-bit word-width 64-point FFT/IFFT processor developed primarily for the application in an OFDM-based IEEE 802.11a wireless LAN baseband processor. The 64-point FFT is realized by decomposing it into a two-dimensional structure of 8-point FFTs. This approach reduces the number of required complex multiplications compared to the conventional radix-2 64-point FFT algorithm. The complex multiplication operations are realized using shift-and-add operations. Thus, the processor does not use a two-input digital multiplier. It also does not need any RAM or ROM for internal storage of coefficients. The proposed 64-point FFT/IFFT processor has been fabricated and tested successfully using our in-house 0.25-/spl mu/m BiCMOS technology. The core area of this chip is 6.8 mm/sup 2/. The average dynamic power consumption is 41 mW at 20 MHz operating frequency and 1.8 V supply voltage. The processor completes one parallel-to-parallel (i.e., when all input data are available in parallel and all output data are generated in parallel) 64-point FFT computation in 23 cycles. These features show that though it has been developed primarily for application in the IEEE 802.11a standard, it can be used for any application that requires fast operation as well as low power consumption.

Three-dimensional nonlinear image reconstruction for microwave biomedical imaging

Abstract: Active microwave imaging has attracted significant interests in biomedical applications, in particular for breast imaging. However, the high electrical contrasts in breast tissue also increases the difficulty of forming an accurate image because of the increased multiple scattering. To model such strong three-dimensional (3-D) multiple scattering effects in biomedical imaging applications, we develop a full 3-D inverse scattering algorithm based on the combination of the contrast source inversion and the fast Fourier transform algorithm. Numerical results show that our algorithm can accurately invert for the high-contrast media in breast tissue.

Rewriting Variables: The Complexity of Fast Algebraic Attacks on Stream Ciphers

Abstract: Recently proposed algebraic attacks [2,6] and fast algebraic attacks [1,5] have provided the best analyses against some deployed LFSR-based ciphers. The process complexity is exponential in the degree of the equations. Fast algebraic attacks were introduced [5] as a way of reducing run-time complexity by reducing the degree of the system of equations. Previous reports on fast algebraic attacks [1,5] have underestimated the complexity of substituting the keystream into the system of equations, which in some cases dominates the attack. We also show how the Fast Fourier Transform (FFT) [4] can be applied to decrease the complexity of the substitution step. Finally, it is shown that all functions of degree d satisfy a common, function-independent linear combination that may be used in the pre-computation step of the fast algebraic attack. An explicit factorization of the corresponding characteristic polynomial yields the fastest known method for performing the pre-computation step.

Simulation methods for linear fractional stable motion and farima using the fast fourier transform

Abstract: We present efficient methods for simulation, using the Fast Fourier Transform (FFT) algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely, (i) the linear fractional stable motion (LFSM) process and (ii) the fractional autoregressive moving average (FARIMA) time series with SαS innovations. These two types of heavy-tailed processes have infinite variances and long-range dependence and they can be used in modeling the traffic of modern computer telecommunication networks. We generate paths of the LFSM process by using Riemann-sum approximations of its SαS stochastic integral representation and paths of the FARIMA time series by truncating their moving average representation. In both the LFSM and FARIMA cases, we compute the involved sums efficiently by using the Fast Fourier Transform algorithm and provide bounds and/or estimates of the approximation error. We discuss different choices of the discretization and truncation parameters involved in our algorithms and illustr...

Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers

Abstract: We present a new algorithm for calculation of the band structure of photonic crystal slabs. This algorithm combines the plane-wave expansion method with perfectly matched layers for the termination of the computational region in the direction out of the plane. In addition, the effective-medium tensor is applied to improve convergence. A general complex eigenvalue problem is then obtained. Two criteria are presented to distinguish the guided modes from the PML modes. As such, this scheme can accurately determine the band structure both above and below the light cone. The convergence of the algorithm presented has been studied. The results obtained by using this algorithm have been compared with those obtained by the finite-difference time-domain method and found to agree very well.

Desynchronized Processing technique for Harmonic and interharmonic analysis

Abstract: A new desynchronized processing technique for harmonic and interharmonic analysis that has general validity and results fully compatible with the IEC standard is presented This technique is based on a double-stage signal processing procedure: In the first stage, the harmonic components are accurately estimated via interpolations in frequency domain and filtered away from the original signal so that in the second stage, interharmonics can be evaluated without the spectral leakage due to harmonic tones Since the procedure does not require synchronization, it allows adopting a fixed sampling frequency and, at the same time, the direct use of fast Fourier transform on the acquired samples, thereby reducing the computational burden The procedure is successfully applied to both numerical tests and onfield measurements The obtained results are as accurate as those of synchronized techniques

Option pricing using the fractional FFT

Abstract: This paper shows how the recently developed fractional FFT algorithm (FRFT) can be used to retrieve option prices from the corresponding characteristic functions. The FRFT algorithm has the advantage of using the characteristic function information in a more efficient way than the straight FFT. Typically, therefore, fewer function evaluations are needed and substantial savings in computational time can be made. Two experiments, based on the stochastic volatility and the variance-gamma models, illustrate the benefits of using the fractional version of the FFT and show that option prices can be delivered up to 45 times faster without substantial loss of accuracy in the results.

Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms.

Abstract: We present a procedure using continuous wavelet transforms (CWTs) to extract the phase information from moire interferograms. The relationship between precise ridge detection of the two-dimensional CWT magnitude map and accurate phase extraction is detailed. A cost function is introduced for the adaptive selection of the ridge, and a computationally inexpensive implementation of the cost function ridge detection algorithm is explored with dynamic programming optimization. The results of the proposed ridge detection algorithm on actual interferograms are illustrated. Moreover, the resulting extracted phase is demonstrated to be smooth and accurate. As a result, the sensitivity of the moire interferometry method is improved to obtain a pixel-by-pixel in-plane strain distribution map.

A dynamic scaling FFT processor for DVB-T applications

Abstract: This paper presents an 8192-point FFT processor for DVB-T systems, in which a three-step radix-8 FFT algorithm, a new dynamic scaling approach, and a novel matrix prefetch buffer are exploited. About 64 K bit memory space can be saved in the 8 K point FFT by the proposed dynamic scaling approach. Moreover, with data scheduling and pre-fetched buffering, single-port memory can be adopted without degrading throughput rate. A test chip for 8 K mode DVB-T system has been designed and fabricated using 0.18-/spl mu/m single-poly six-metal CMOS process with core area of 4.84 mm/sup 2/. Power dissipation is about 25.2 mW at 20 MHz.

Signal-processing algorithm for white-light optical fiber extrinsic Fabry–Perot interferometric sensors

Abstract: We present a novel signal-processing algorithm for single-mode optical fiber extrinsic Fabry–Perot interferometric sensors that can achieve both high-resolution, absolute measurement of the cavity length and a large dynamic measurement range simultaneously. The algorithm is based on an accurate model of the characteristics of a fiber-optic sensor that takes into account the phase shift that is due to the coupling of light reflected at the second surface to the lead-in fiber end.

Disturbance classification utilizing dynamic time warping classifier

Abstract: The application of deregulation policies in electric power systems results in the absolute necessity to quantify power quality. This fact highlights the need for a new classification strategy which is capable of tracking, detecting, and classifying power-quality events. In this paper, a new classification approach that is based on the dynamic time warping (DTW) algorithm is proposed. The new algorithm is supported by the vector quantization (VQ) and the fast match (FM) techniques to speed up the classification process. The Walsh transform (WT) and the fast Fourier transform (FFT) are adopted as feature extraction tools. The application of the combined fast match-dynamic time warping (FM-DTW) algorithms provides superior results in speed and accuracy compared to the traditional artificial neural networks and fuzzy logic classifiers. Moreover, the proposed classifier proves to have a very low sensitivity to noise levels.

Incorporating a psychoacoustical model in frequency domain speech enhancement

Abstract: A frequency domain optimal linear estimator is proposed which incorporates the masking properties of the human auditory system to make the residual noise distortion inaudible. The use of wavelet-thresholded multitaper spectra is also proposed for frequency-domain speech enhancement methods as an alternative to the traditional fast Fourier transform (FFT)-based magnitude spectra. Experiments with multitalker babble noise indicated that the proposed estimator outperformed the minimum mean-square error log-spectral amplitude estimator (MMSE-LSA), particularly when wavelet-thresholded multitaper spectra were used in place of the FFT spectra.

Signal processing system for satellite positioning signals

Abstract: A signal processing system for processing satellite positioning signals is described The system comprises at least one processor and a signal processor operating under a number of operational modes The signal processor includes at least one of a signal processing subsystem, a fast Fourier transform (FFT) subsystem, and a memory subsystem that are each dynamically and independently configurable in response to the operational modes Further, the system includes a controller that couples to control transfer of data among the signal processing subsystem and the FFT subsystem via the memory subsystem Configurability of the memory subsystem includes configuring the memory subsystem into regions according to the operational modes where each region is accessible in one of a number of manners according to the operational modes

Improving FFT Frequency Measurement Resolution by Parabolic and Gaussian Spectrum Interpolation

Abstract: Discrete spectra can be used to measure frequencies of sinusoidal signal components. Such a measurement consists of digitizing a compound signal, performing windowing of the signal samples and computing their discrete magnitude spectrum, usually by means of the Fast Fourier Transform algorithm. Frequencies of individual components can be evaluated from their locations in the discrete spectrum with a resolution depending on the number of samples. However, the frequency of a sinusoidal component can be determined with improved resolution by fitting an interpolating parabola through the three largest consecutive spectrum bins corresponding to the component. The abscissa of its maximum constitutes a better frequency approximation. Such a method has been used for tune measurement systems in circular accelerators. This paper describes the efficiency of the method, depending on the windowing function applied to the signal samples. A typical interpolation gain is one order of magnitude. Better results are obtained with Gaussian interpolation, offering frequency resolution improvement by more than two orders of magnitude when used with windows having fast sidelobe decay. An improvement beyond three orders of magnitude is possible with steep Gaussian windows. These results are confirmed by laboratory measurements. Both methods assume the measured frequency to be constant during acquisition and the spectral peak corresponding to the measured component to constitute a local maximum in a given band of the input signal discrete spectrum.

A frequency multiplexed near infra-red topography system for imaging functional activation in the brain

Abstract: We have developed a novel near-infrared optical topography system that can acquire images at 10 frames per second. It uses frequency multiplexed sources, and FFT detection.

The stable downward continuation of potential field data

Abstract: Filtering methods based on the Fourier transform are routinely used in the processing of geophysical data. Because of the nature of the Fourier transform, the data must be prepared before the transform is calculated. This preparation usually takes the form of the removal of any trend from the data, combined with the padding of the data to 2 N points between the data edges. However, no data preparation procedure is perfect, and the result is that problems (in the form of edge effects) appear in the filtered data. When high-pass filters (such as derivatives or downward continuation) are subsequently used, then these edge effects become particularly apparent. This paper suggests three methods for the stable downward continuation of geophysical data (two of which may be combined). The first method is applied to an integrated horizontal derivative of the data rather than to the data itself. Since the horizontal derivative can be calculated in the space domain where fast Fourier transform (FFT) edge effects are not present, this reduces the enhancement of the data at frequencies near the Nyquist, resulting in smaller edge effect problems. The second method measures the FFT-induced noise by comparing data that has been downward continued using both the space- and frequency-domain methods. The data is then compensated accordingly, and the compensated data may be downward continued to arbitrary distances that are not possible using space-domain operators. The final method treats downward continuation as an inverse problem, which allows the control of both FFT-induced noise and other noise that is intrinsic to the dataset. This method is computationally slow compared to the first two methods because of the inversion of large matrices that is required. The methods are demonstrated on synthetic models and on aeromagnetic data from the Bushveld igneous complex, South Africa.

A fast physical optics (FPO) algorithm for high frequency scattering

Abstract: A novel algorithm referred as the fast physical optics (FPO) for computing the back-scattered field over a range of aspect angles and frequencies is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency scattering regime. The proposed algorithm is, also, directly applicable to fixed angle bistatic configurations and a variety of single scattering formulations. The method comprises two steps. First, a decomposition of the scatterer into subdomains and computation of the pertinent scattering characteristics of each subdomain. Second, interpolation, phase-correction and aggregation of the scattering patterns of the subdomains into the final pattern of the whole body. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT. The proposed method is especially suited for generation of synthetic data for radar imaging simulation.

Large-scale broad-band parasitic extraction for fast layout verification of 3-D RF and mixed-signal on-chip structures

Abstract: A methodology for efficient parasitic extraction and verification flow for RF and mixed-signal integrated-circuit designs is presented. The implementation of a multiplane precorrected fast Fourier transform (PFFT) computational engine enables the full-wave electromagnetic (EM) simulation of interconnects and passive components. The PFFT algorithm is implemented on a set of two-dimensional fast Fourier transform grids associated with the current sheets corresponding to the conductor loss models. This leads to the full-wave modeling of silicon embedded three-dimensional circuits within the two-and-one-half-dimensional computational framework yielding the O(NlogN) computational complexity and O(N) memory requirements of the algorithm. The broad-band capability of the EM solver is provided through the loop-tree/charge implementation of the PFFT algorithm allowing for robust full-wave modeling from dc to microwaves. The EM verification flow is integrated seamlessly within the Cadence environment allowing for the nonlinear circuit simulation of the entire device. The capability and accuracy of the proposed methodology is demonstrated through EM simulation results for an individual on-chip spiral inductor, as well as a low-noise amplifier.