Showing papers on "Fast Fourier transform published in 1973"

Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform

Abstract: A lower bound for the number of additions necessary to compute a family of linear functions by a linear algorithm is given when an upper bound c can be assigned to the modulus of the complex numbers involved in the computation. In the case of the fast Fourier transform, the lower bound is (n/2) log2n when c = 1.

Parallelism in fast Fourier transform hardware

Abstract: The fast Fourier transform algorithm is derived by means of successive fracturing of one-dimensional data strings into two-dimensional arrays. Using this formulation, a diagrammatic representation of mixed radix and highest radix FFT algorithms is derived. Using this representation, two broad classes of FFT hard-ware are explored, from the point of view of speed, parallelism, radix number, and type of memory.

The Application of the Fast Fourier Transform to Electrical Transient Phenomena

Abstract: There are many kinds of digital calculation methods for transient phenomena on a electrical system. The most highly developed technique among them is the iterative method of travelling waves which has been given as the O'Alembert's solution of the wave equation. The technique was first devised by Schnyder! and Bergeron\" and developed by Frey3 , Barthold , McElroy 5, Ametani\" and others. The other famous technique is the Fourier transform which is based on the Bernoulli's solution of the wave equation. This technique has been developed by Leg0 , Mullineux\", Wedepohl? and others. This, however, has a severe disadvantage, that is, computer programs are using hundreds of hours of computer time with procedures requiring N 2 operations to compute Fourier transforms of N data points.

Simulation of Multicorrelated Random Processes Using the FFT Algorithm

Abstract: A technique for the digital simulation of multicorrelated Gaussian random processes is described. This technique is based upon generating discrete frequency functions which correspond to the Fourier transform of the random processes and then using the fast Fourier transform (FFT) algorithm to obtain the actual random processes. The main advantage of this method over other methods is computation time; it appears to be more than an order of magnitude faster than present methods of simulation. One of the main uses of multicorrelated simulated random processes is in solving nonlinear random vibration problems by numerical integration of the governing differential equations. [This research is supported in part by NASA.]

Damped vibration mode superposition method for dynamic response analysis

Abstract: In the dynamic response analysis of extremely complex structural systems in which the damping characteristics of each element are independent, the damping matrix is not always diagonalized by the use of undamped free vibration mode shapes In the present paper, a mode-superposition method by the use of damped free vibration mode shapes is developed for such structural systems It is also shown that the Fast Fourier Transform (FFT) procedures, that are available for the dynamic response analysis of linear structural systems, are used effectively in this mode-superposition method with good accuracy

Method and apparatus for addressing FFT processor

Abstract: Method and apparatus for reducing the hardware requirements and complex control of an in-place Fast Fourier Transform (FFT) processor by a unique repetitive arrangement of the stored data pattern of N complex data points or record samples in the same predetermined order each time after each iteration or pass of the data through an FFT arithmetic unit. This results in the final output sequence of the calculated data points automatically having the same format as the initial input sequence. Four data memories are utilized in pairs in conjunction with the arithmetic unit wherein the calculated samples are stored in successive iterations. For example, the first pair of memory units are selectively addressed for receiving the calculated results in a predetermined order and then used as the input means for consecutively feeding its contents to the arithmetic unit in the next pass at which time the second pair of memories are selectively addressed in the same predetermined manner for storing the calculated data. Thus the memories alternate as input and output memory devices always having the data stored therein in the same predetermined order while having a subsequent serial readout.

Fourier Transform vs Hadamard Transform Spectroscopy

Abstract: Recent articles have claimed a significant S/N advantage of Hadamard transform spectroscopy over Fourier transform spectroscopy. The scanty published data does not support this assertion, and the possibility that the claim is valid in theory is examined. Existing theory, as reported in the literature, is not consistent with the claims made for the technique. The advantages and drawbacks of Hadamard transform spectroscopy are examined in detail.

Redundant fast fourier transform data handling computer

Abstract: Special purpose data handling equipment is utilized with a fast Fourier transform algorithm computer. The equipment buffers input data such that each block of input data includes data from the immediately preceding and following data blocks. This input redundancy is useful when input data is processed through a data window which attenuates data at the beginning and end of the data block, since, when this data is transformed and subsequently inversely transformed, simple addition of the output data points removes the effect of the attenuating window.

Cooley-Tukey-type algorithm for the Haar transform

Abstract: It is shown that the Haar transform can be computed using a Cooley-Tukey-type algorithm that is implemented in 2(N−1) additions/subtractions. This algorithm is derived by relating the Haar transform to the modified Walsh-Hadamard transform using a simple bit-reversal scheme.

Scattering−matrix description and nearfield measurements of electroacoustic transducers

Abstract: Recently developed analytical techniques for the measurement of microwave antennas at reduced distances are “translated” into corresponding techniques for the measurement of electroacoustic transducers in fluids. The basic theory is formulated in scattering‐matrix form and emphasizes the use of plane‐wave spectra for the representation of sound fields. This theory, in contrast to those based on asymptotic description of transducer characteristics, is suitable for the formulation and solution of problems involving interactions at arbitrary distances. Two new techniques (in particular) are described: One, utilizing deconvolution of transverse scanning data, which may be taken at distances d much less than the Rayleigh distance dR(≡ a2/2λ), provides a means of obtaining complete effective directivity functions, corrected for the effects of the measuring transducer. Applicability of a (two‐dimensional, spatial) sampling theorem and the “fast Fourier transform” algorithm, which greatly facilitate the necessary...

A class of finite computation structures supporting the fast fourier transform

Abstract: : The paper presents several results relating modular arithmetic schemes and the Fast Fourier transform. In particular, the classes of modular rings of integers in which the FFT may be computed is completely characterized by the prime decomposition of the modulus. Also, an extension of this result for computation structures similar to modular rings of integers yields a sufficiency hypothesis for the computation of FFT.

On the Numerical Reconstruction of Images from a Microwave Hologram

Abstract: A new technique for the numerical reconstruction of images from a long-wavelength hologram is proposed. The technique is to calculate images by the fast Fourier transform (FFT) algorithm with the hologram data sampled by a straight line approximation. This sampling technique is convenient to reduce the number of the sampling points, and the image can be reconstructed with less data than the conventional equally spaced sampling method. A one-dimensional hologram is constructed at S band and an image is reconstructed by the proposed method. These results are discussed and compared with the results of the conventional numerical reconstruction.

Computer optimization of the fraction of labelled mitoses analysis using the fast Fourier transform.

Abstract: This paper provides a numerical technique for the solution of the fraction of labelled mitoses curve. The essence of the method is to facilitate convolutions of phase time distributions using the FFT. This FFT method, in conjunction with the optimization technique, is found to be an efficient, general procedure.

On the Twiddling Factors

Abstract: Concepts of group theory are used to explain the difference between two major fast Fourier transform (FFT) algorithms and the relation between FFT and fast Walsh transforms.

The SPS-41 and SPS-81 programmable digital signal processors

Abstract: The SPS-41 and SPS-81 are very high speed multiprocessor computers designed for signal processing applications. They can either function as stand-alone processors or operate in conjunction with a conventional computer. The SPS-41 provides the capability to perform signal processing functions with about a 100 fold increase in speed over a conventional computer—typically 8.3 milliseconds for a 1024 complex Fast Fourier Transform. The SPS-81 is roughly twice as fast as the SPS-41. This speed is achieved through a highly parallel architecture which is optimized for signal processing operations.

A Computer Utility Incorporating the FFT Algorithm for a Signal and System Theory Course

Abstract: One of the problems in effectively teaching a course in signal and system theory is the difficulty of performing the mathematical operations involved in the application of theory to meaningful problems. In theory, the Fourier transform, convolution and correlation operations usually are readily grasped by the student but the application often proves to be difficult. Performing the integral operations requires painstaking care to get proper limits on the integrals, displacing functions properly, etc. It seems that the student gains little insight to the problem under analysis by these manipulations. Typically, only the simplest type of functions are handled by this analytic approach. This paper describes the Signal Analysis Program, a computer utility which employs the Fast Fourier Transform (FFT) algorithm and is designed to relieve the user from time consuming and tedious calculations. Classes of problems and signal functions, previously deemed too complicated to treat in an undergraduate course, require little more concern than the simplest of problems. The effectiveness and applicability of this utility has been demonstrated by students applying it to many other areas where it is not a course requirement.

On Digital Simulation of Multicorrelated Random Processes and Its Applications

Abstract: Two methods are described to simulate, on a digital computer, a set of correlated, stationary, and Gaussian time series with zero mean from the given matrix of power spectral densities and cross spectral densities. The first method is based upon trigonometric series with random amplitudes and deterministic phase angles. The random amplitudes are generated by using a standard random number generator subroutine. An example is given which corresponds to three components of wind velocities at two different spatial locations for a total of six correlated time series. In the second method, the whole process is carried out using the Fast Fourier Transform approach. This method gives more accurate results and works about twenty times faster for a set of six correlated time series.

The walsh transform—a new tool for control engineers

Abstract: An introduction is given to the generation and use of new transform techniques which have important applications in binary control and processing methods. A comparison is made between the fast Fourier transform and the equivalent fast Walsh transform together with the steps required to produce a transform algorithm and computer program. Some applications of the transform are then discussed and which include spectral analysis, filtering, non‐linear control and communications uses. 18 references to current work in these applications areas are included.

Minimum-Bias Windows for Spectral Estimation by Means of Overlapped Fast Fourier Transform Processing

Abstract: : The time-limited nonnegative data windows that minimize the bias in auto- and cross-spectral estimation of stationary random processes by means of overlapped Fast Fourier Transform (FFT) processing are derived for a variety of constraints. The author constrains the time duration of the data window, or constrain the bandwidth in various ways, such as the equivalent-noise bandwidth, the half-power bandwidth, or the root-mean-square bandwidth. In the three bandwidth-constrained cases, the window duration is adjusted to meet the constraint. We find that the Hanning window is a reasonable compromise for achieving minimum bias, because in addition to being the optimum for one bandwidth constraint, it is very close to the optima for two other bandwidth constraints. The relative merits of the spectral characteristics of the windows are also discussed.

A Projected Gradient Method for Automatic Equalization in the Discrete Frequency Domain

Abstract: In a recent paper [1] we reported on a new mean-square error automatic equalizer utilizing Rosen's gradient projection theorem to optimize parameters in the discrete frequency domain. Here we develop another projection method to optimize the discrete frequency parameters. The algorithm converges (in the mean) for any channel, even in the presence of noise. It is shown that for the channels considered, convergence is equivalent to comparable time domain equalizers. The method makes use of fast Fourier transform (FFT) algorithms for computation of the iteration matrix, the gradient, and the projection operation. Use of the FFT for parameter iterations reduces the necessary computations per parameter to a number proportional to log_{2} M compared to M for a time domain equalizer, where M is the number of equalizer parameters. The method results in fewer computations per parameter for each iteration, but a somewhat slower rate of convergence than the method employing Rosen's gradient projection.

Analysis for instrument lag and for smoothing

Abstract: Deals with the deconvolution of the response by fast Fourier transform and matrix inversion techniques.

Some new results on a class of periodically varying systems

Abstract: The analysis and stability properties of a special class of R-L-C network, where the energy storage elements vary periodically with time and the dissipative elements are held constant, is discussed. In the analysis, fast Fourier transform technique has been utilized to obtain rapidly an accurate response of the network when excited by any arbitrary periodic signal. In the stability results, it has been shown that the network's stability can be ensured in a very simple manner if the connection matrix of the network is in Jordan normal form.

Fast Fourier Transform with Computer Program

Abstract: Many computer programs have been developed to calculate the Fast Fourier Transform (FFT). It is the intention of this thesis to develop the tree graph idea, presented by E. 0. Brigham and R. E. Morrow in the article "The fast Fourier transform," into another computer program that will calculate both the forward and inverse Fourier transforms using nonsymmetrical periodic functions. Most of the information obtained was from periodicals with relatively little available in text books. General matrix equations and calculations presented in proofs were developed by this thesis. The tree graph idea was also expanded to a general form. First the matrix equations for the Discrete Fourier Transform (DFT) were developed. Starting with the Fourier transform pair for an aperiodic continuous function and the matrix equations for the DFT, steps were taken to show how these equations were tied together. Two methods for the FFT wereeevaluated and proven equal to the DFT matrix equations. The more efficient method was written into a computer program which was explained in detail. Finally examples using this computer program were presented. The forward FFT was approximated using input functions such as a rectangular wave, a step function, a sawtooth wave, and a constant. A test for accuracy was also presented using a rectangular wave input time function.

On the fast computing of three-dimensional Fourier transforms of crystallographic data via external storage

Abstract: Fast Fourier Transforms (FFT) are widely known as useful tools for the evaluation of spectral data. This article discusses the applicability of FFT methods to crystallographic problems. Formulae are derived which make it possible to use fast Fourier transforms for the general Fourier summation of crystallographic data in all space groups and for the computation of slant planes at arbitrary positions in the unit cell. As even moderate resolutions would produce arrays of data too large to fit within internal computer memory, they must be kept to an external storage device. The organization of data and the resulting time requirements are thoroughly discussed. An ALGOL 60 program has been developed with as many redundancies eliminated as possible. An example shows that for a problem of moderate size this algorithm is faster by an order of magnitude than those which have traditionally been used.

Statistical Evaluation of Time Series Analysis Techniques

Abstract: The performance of a modified version of NASA's multivariate spectrum analysis program is discussed. A multiple regression model was used to make the revisions. Performance improvements were documented and compared to the standard fast Fourier transform by Monte Carlo techniques.

Digital processing of radiographic images

Abstract: Some techniques are presented and the software documentation for the digital enhancement of radiographs. Both image handling and image processing operations are considered. The image handling operations dealt with are: (1) conversion of format of data from packed to unpacked and vice versa; (2) automatic extraction of image data arrays; (3) transposition and 90 deg rotations of large data arrays; (4) translation of data arrays for registration; and (5) reduction of the dimensions of data arrays by integral factors. Both the frequency and the spatial domain approaches are presented for the design and implementation of the image processing operation. It is shown that spatial domain recursive implementation of filters is much faster than nonrecursive implementations using fast fourier transforms (FFT) for the cases of interest in this work. The recursive implementation of a class of matched filters for enhancing image signal to noise ratio is described. Test patterns are used to illustrate the filtering operations. The application of the techniques to radiographic images of metallic structures is demonstrated through several examples.