Showing papers on "Fast Fourier transform published in 1988"

The fast Fourier transform and its applications

Abstract: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

Fault-tolerant FFT networks

Abstract: Two concurrent error detection (CED) schemes are proposed for N-point fast Fourier transform (FFT) networks that consists of log/sub 2/N stages with N/2 two-point butterfly modules for each stage. The method assumes that failures are confined to a single complex multiplier or adder or to one input or output set of lines. Such a fault model covers a broad class of faults. It is shown that only a small overhead ratio, O(2/log/sub 2/N) of hardware, is required for the networks to obtain fault-secure results in the first scheme. A novel data retry technique is used to locate the faulty modules. Large roundoff errors can be detected and treated in the same manner as functional errors. The retry technique can also distinguish between the roundoff errors and functional errors that are caused by some physical failures. In the second scheme, a time-redundancy method is used to achieve both error detection and location. It is sown that only negligible hardware overhead is required. However, the throughput is reduced to half that of the original system, without both error detection and location, because of the nature of time-redundancy methods. >

Survey of excitation signals for FFT based signal analyzers

Abstract: The properties of ten different excitation signals are studied to analyze their suitability as excitation signals for fast Fourier transform (FFT)-based signal and network analyzers. Their influence on the measurement time, accuracy, and sensitivity to nonlinear distortions is described. The flexibility to create a customized amplitude spectrum is investigated. With this information it becomes possible to select the best excitation signal for many applications. >

Abel inversion using fast Fourier transforms.

Abstract: A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Handbook of Digital Signal Processing: Engineering Applications

Abstract: D.F. Elliott, Transforms and Transform Properties. P.P. Vaidyanathan, Design and Implementation of Digital FIR Fil ters. F.J . Harr is, Multirate FIR Filters for Interpolating and Desampling. N.A. Pashtoon, IIR Digital Filters. P.P. Vaidyanathan, Low-Noise and Low-Sensitivity Digital Filters. P. Yip and K.R. Rao, Fast Discrete Transforms. D.F. Elliott, Fast Fourier Transforms. F.J. Harris, Time Domain Signal Processing with the DFT. J.A. Cadzow, Spectral Analysis. M.T. Silvia, Deconvolution. M.T.Silvia, Time Delay Estimation. N. Ahmed, Adaptive Filtering. G.H. Hostetter, Recursive Estimation. L. Mintzer, Mechanization of Digital Signal Processors. F.J. Harris, Window Generation Computer Program. Each chapter includes references. Index.

Calculation of an OMIT map

Abstract: A space-group-general computer program to compute an OMIT map using fast Fourier transforms is presented. In this procedure an asymmetric unit of the unit cell is divided into several boxes. For each box a set of phases is calculated by the inverse Fourier transforms of the existing electron density distribution which has been modified so that the electron density values in and around that box is a constant. An OMIT map is then calculated for each box by the Fourier transforms of the observed amplitudes with these phases. The computer program may be used to reduce bias in electron density maps during model building and refinement of macromolecules. The procedure was used to detect error in the atomic model of a derivative of ribonuclease (personal communication by J. Nachman, National Cancer Institute, Frederick, Maryland, USA).

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part II: Methods and results.

Abstract: Various alternative spectral estimation methods are examined and compared in order to assess their possible application for real-time analysis of Doppler ultrasound arterial signals. Specifically, five general frequency domain models are examined, including the periodogram, the general autoregressive moving average (ARMA) model which has the autoregressive (AR) and moving average (MA) models as special cases, and Capon's maximum likelihood spectral model. A simulated stationary Doppler signal with a known theoretical spectrum was used as the reference test sequence, and white noise was added to enable various signal/noise conditions to be created. The performance of each method representative of each spectral model was assessed using both qualitative and quantitative schemes that convey information related to the bias and variance of the spectral estimates. Three integrated performance indices were implemented for quantitative analysis. The relative computational complexity for each algorithm was also investigated. Our results indicate that both the AR(Yule-Walker) and ARMA(singular value decomposition) models of orders (8) and (4, 4), respectively, show good agreement with the theoretical spectrum, and yield estimates with variances considerably less than the Fast Fourier Transform (FFT). Preliminary results obtained with these methods using a clinical, non-stationary Doppler signal supports these observations.

A fault-tolerant FFT processor

Abstract: A method is proposed for achieving fault tolerance by introducing a redundant stage for a special-purpose fast Fourier transform (FFT) processor. A concurrent error-detection technique, called recomputing by alternate path, is used to detect errors during normal operation. Once an error is detected, a faulty butterfly can be located with log (N+5) additional cycles. The method has 100% detection and location capability, regardless of the magnitude of the roundoff errors. A gracefully degraded reconfiguration using a redundant stage is introduced. This technique ensures a high improvement in reliability and availability. Hardware overhead is O(1/log N) with some additional comparators and switches. The method can be applied to other algorithms implementable on the butterfly structure. >

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part I: Estimation methods.

Abstract: When compared to the classical Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) approach, modern estimation methods offer the potential for achieving significant improvements in estimating the power density spectrum of Doppler ultrasound signals. Such improvements, for example, might enable minor flow disturbances to be detected, thereby improving the sensitivity in arterial disease assessment. Specifically, reduction in the variance and bias can be achieved, and this may enable disturbed flow to be detected in a more sensitive manner. The approach taken here, is to consider spectral estimation methods as a problem of fitting an assumed model to the Doppler signal. The models described assume that the signal is stationary. Since the Doppler signal is generally nonstationary, it is assumed that a short enough time window interval can be chosen over which the signal can be considered stationary. We shall review the various methods and when appropriate, relate them to the nature of the Doppler signal.

The relationship between tapped delay-line and FFT processing in adaptive arrays

Abstract: The use of fast Fourier transform (FFT) processing behind the elements in adaptive arrays is often considered as a means of improving the nulling bandwidth of such arrays. However, it is shown that the output signal-to-interference-plus-noise ratio obtained from an adaptive array with FFTs behind the elements is identical to that of an equivalent adaptive array with tapped delay-line processing. The equivalent tapped delay-line array has the same number of taps in each delay line as the number of time samples in the FFTs, and has a delay between taps equal to the delay between samples in the FFTs. Thus, while the bandwidth performance of an adaptive array can be improved by using time-delayed samples of each element signal, no further improvement results from taking FFTs of these sampled signals. The same bandwidth performance is obtained by simply weighting and combining the time-domain samples directly. >

A new efficient algorithm to compute the two-dimensional discrete Fourier transform

Abstract: An algorithm is presented for computation of the two-dimensional discrete Fourier transform (DFT). The algorithm is based on geometric properties of the integers and exhibits symmetry and simplicity of realization. Only one-dimensional transformation of the input data is required. The transformations are independent; hence, parallel processing is feasible. It is shown that the number of distinct N-point DFTs needed to calculate N*N-point two-dimensional DFTs is equal to the number of linear congruences spanning the N*N grid. Examples for N=3, N=4, and N=10 are presented. A short APL code illustrating the algorithm is given. >

Fast Hartley transforms for image processing

Abstract: The fast Hartley transform (FHT) is used to transform two-dimensional image data. Because the Hartley transform is real-valued, it does not require complex operations. Both spectra and autocorrelations of two-dimensional ultrasound images of normal and abnormal livers were computed. >

A scheme to analyze conducting plates of resonant size using the conjugate-gradient method and the fast Fourier transform

Abstract: A scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate-gradient (CG) method and the fast Fourier transform (FFT) is presented in detail. The problems are analyzed by solving their corresponding electric-field integral equation. The procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields. These functions have been widely used in moment-method (MM) applications. The scheme is an efficient numerical tool, benefiting from the good convergence and low memory requirements of the CG and the low CPU time consumed in performing convolutions with the FFT. In comparison with the MM, the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude. Several results are presented and compared with analytical, numerical, or measured values that appear in the literature. >

Computationally efficient sine-wave synthesis and its application to sinusoidal transform coding

Abstract: A technique for sine-wave synthesis is described that uses the fast Fourier transform overlap-add method at a 100 Hz rate based on sine-wave parameter coded at a 50 Hz rate. This technique leads to an implementation requiring less than one-half the computational power of a digital-signal-processor chip. The synthesis method implicitly introduces a frequency jitter which renders the encoded synthetic speech more natural. For speech computed by additive acoustic noise, the synthesizer, in conjunction with straightforward noise suppression, greatly improve the quality of the synthetic speech, rendering the sinusoidal transform coder (STC) algorithm a truly robust system. More recent architecture studies of the STC algorithm suggests that an entire implementation requires no more than two ADSP2 100 chips. >

Spectral analysis of muscular sound at low and high contraction level.

Abstract: The activated muscle generates a low frequency rumbling noise, which is known as the Sound-MyoGram (SMG). Spectral analysis of the SMG is carried out in this work, in order to: (i) check the adequacy of both the Fast Fourier Transform (FFT) and the Maximum Entropy Spectrum Estimation (MESE). Because it is a well known technique, the FFT method is only briefly described, while the philosophy of the MESE method is given in more detail and completed with a description of the recursive algorithm; (ii) select a frequency parameter suitable to describe the SMG. For this purpose two well-defined physiological conditions (20% and 80% Maximal Voluntary Contraction) have been adopted in order to provide a safe reference for the interpretation of the findings. The results show that: (a) both FFT and MESE are adequate to estimate the SMG Power Spectrum; (b) both the mean and the median frequency are suitable parameters, the mean frequency being the more favourable one; (c) the SMG Power Spectrum is a promising tool to study the muscle activation modalities.

Flat-top windows for PWM waveform processing via DFT

Abstract: New flat-top windows by which per forming the measurement of the parameters that characterise periodic signals are presented. It is shown how, by applying these windows in the frequency domain beyond the FFT, the negative effects of both the spectral leakage and the harmonic interference are reduced without employing interpolation algorithms. The high accuracy of the results is confirmed by an error analysis. These windows are very useful in the determination of the harmonic content of the inverter output PWM waveforms supplying electrical motors, in order to qualify the entire drive.

A High-Performance FFT Algorithm for Vector Supercomputers

Abstract: Many traditional algorithms for computing the fast Fourier transform FFT on conventional computers are unacceptable for advanced vector and parallel computers because they involve nonunit, power-of-two memory strides. This paper presents a practical technique for computing the FFT that avoids all such strides and ap pears to be near-optimal for a variety of current vector and parallel computers. Performance results of a pro gram based on this technique are presented. Notable among these results is that a Fortran implementation of this algorithm on the CRAY-2 runs up to 77% faster than Cray's assembly-coded library routine.

Pipelined combination and vector signal processor

Abstract: A digital array signal processor and an associated method are described for implementing the fast Fourier transform radix-4 butterfly algorithm. The digital array signal processor is an integrated circuit with a four stage pipeline and can perform a radix-4 butterfly operation on four complex operands every 80 nanoseconds. Using the decimation-in-frequency implementation of the radix-4 butterfly algorithm, the digital array signal processor includes a first stage for distribution of complex input operand values, a second stage for performing addition and subtraction operations, a third stage for performing multiplication operations and a fourth stage for distribution of the output operand values. The digital array signal processor can be reconfigured to perform a radix-2 butterfly operation on two sets of two complex numbers during the 80 nanosecond machine cycle as well as frequently used arithmetic and logic operations. The digital signal array processor can be configured to perform a series of operations on an array of operands or can be one of a series of processors, each processor performing a separate operation on an operand array. According to a second implementation, the digital array signal processor can perform the radix-4 butterfly algorithm using the decimation-in-time algorithm.

Combinatorial logic based digital optical computing architectures

Abstract: Most of the compute intensive SDI problem solving processors rely on a common set of algorithms found in numerical matrix algebra. Typically, all these problems are broken up into a set of linear equations where it is the processors task to solve this set. Algorithmic solutions range from the extensive use of the fast Fourier transform to the robust singular value decomposition method. Over the past several years considerable research has been focused on the use of arrays of computational processing elements, which, when configured correctly, will process these algorithms at extremely high speeds and with great algorithmic efficiency. To obtain these high speeds hardware development has progressed primarily in two areas: (1) semiconductor VLSI arrays utilizing 2-D planar semiconductor technology and (2) acoustooptic analog and digital arrays utilizing 3-D optical interconnect technology. This paper will focus on the formulation of 3-D optical interconnect methodology for numerical and general purpose binary combinatorial logic based optical computers.

A generalized impulse response model for SAW transducers including effects of electrode reflections

Abstract: Closed-form expressions are presented which describe the behavior of arbitrarily weighted SAW (surface acoustic wave) transducers that contain uniform internal reflections These expressions are based on a coupling-of-modes model of a SAW transducer and are expressed in terms of the Fourier transform of the transducer weighting function with respect to a modified frequency variable This is the same Fourier transform which forms the heart of the conventional impulse response model These transforms are easily evaluated using fast Fourier transform (FFT) routines When the modified frequency variable is mapped back to true frequency, the results are known for all frequencies except a small gap near the center frequency The response in this gap is easily evaluated numerically using expressions which are also given The complete three-port model is then presented in terms of a mixed matrix representation in which the acoustic port variables are of a scattering parameter type and the electrical port variable is of a Y-matrix type >

A wafer-scale 170000-gate FFT processor with built-in test circuits

Abstract: The wafer-scale 170000-gate fast Fourier transform (FFT) processor described consists of individual repeatable building blocks, each of which contains a processing element (PE) and interconnection wiring. The PE consists of a multiplier accumulator and its built-in self-test circuits. The wafer system is reconfigured by connected active blocks after block self-diagnosis. Blocks are connected using a programmable contact-hole mask. The processor performs parallel 16-bit, eight-point complex FFTs and is implemented with 725 I/O pads in triple-metal 2.3- mu m p-well CMOS technology on a 4-in. wafer. It is mounted by controlled-collapse bonding facedown on a 11.8*11.8-cm/sup 2/ substrate. >

An application specific DSP chip set for 100 MHz data rates

Abstract: A 1.2- mu m CMOS chip set (processor and controller) has been designed for applications in high-performance fast Fourier transform (FFT)-based digital signal processing (DSP) systems. The processor chip performs about 500 million arithmetic operations per second and operates at an I/O rate of 5 billion bits per second. The controller chip provides total system control for FFT-based DSP systems. Algorithms such as FFT, spectrum analysis, digital filtering (via frequency domain) can be defined on the chip set by coding 5 to 10 instructions in the controller. Although a single chip set can process data rates at very high speeds (e.g. 1 K FFT in 16 mu s), multiple stages can be cascaded very simply for extremely high performance (up to 100-MHz data rates). >

Gray codes, Fast Fourier Transforms and hypercubes☆

Abstract: Fast Fourier Transforms are a widely-used and powerful tool for the analysis and solution of many problems. They have been used in such diverse areas as medicine, acoustics, image processing, system design and many other fields. By transforming the data the problem may be simpler, more tractable or more efficiently solved and for many applications (e.g. speech processing) the data may be much more easily understood in the transform domain. Therefore fast algorithms for implementing transforms are vital for any powerful computer. This paper describes the implementation of a Fast Fourier Transform on a 64-node INTEL hypercube and shows how the hypercube architecture may be efficiently used. Usually the FFT is only a part of the solution process and the data on the hypercube has to be arranged in a certain manner for the efficient solution of the whole problem. A common way is for the data to be distributed according to a Gray code, so that neighbouring points in the domain are in neighbouring processors. We present a number of results on Gray codes which characterise a certain family of Gray codes, and show that Fast Fourier Transforms on data distributed among processors according to a Gray code can also be efficiently implemented on the hypercube.

The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution

Abstract: The authors consider the further enhancement of the computational efficiency in the electromagnetic scattering of large bodies of revolution (BOR) with a view to making it practical to solve large-body problems. The problem of the electromagnetic scattering of a perfect electrical conducting (PEC) BOR is considered, although the methods provided can be applied to multilayered dielectric bodies. In most methods used, the generation of the elements for the method-of-moments matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements using the fast Fourier transform (FFT). A technique is also presented for extracting the singularity of the Green's function that appears within the integrands of the matrix diagonal. The extraction further enhances the use of the FFT and provides an exact analytic expression. Using this method, the computational time can be improved by at least an order of magnitude for large bodies, compared to existing algorithms. >