Showing papers on "Fast Fourier transform published in 1974"

TDM-FDM Transmultiplexer: Digital Polyphase and FFT

Abstract: The cascading of a discrete Fourier transform processor and a digital polyphase network is shown to reduce the computation rate in frequency multiplexing-demultiplexing systems to a value close to minimum. Implementation advantages of that technique are pointed out. The highest efficiency is achieved when the number of channels is close to a power of 2, which is demonstrated by the 60-channel frequency-division-multiplexing (FDM)-2 × 30-channel time-division-multiplexing (TDM) transmultiplexer; a rough estimate of the computation rate is carried out in a practical case and appears to be quite within reach of the present technological capabilities. Significant cost advantage over equivalent analog equipment is expected. A digital version of the 12-channel FDM system using the same technique is also considered.

Fourier Transform Computers Using CORDIC Iterations

Abstract: The CORDIC iteration is applied to several Fourier transform algorithms. The number of operations is found as a function of transform method and radix representation. Using these representations, several hardware configurations are examined for cost, speed, and complexity tradeoffs. A new, especially attractive FFT computer architecture is presented as an example of the utility of this technique. Compensated and modified CORDIC algorithms are also developed.

TDM-FDM Transmultiplexer: Digital Polyphase and FFT

Abstract: The cascading of a discrete Fourier transform processor and a digital polyphase network is shown to reduce the computation rate in frequency multiplexing-demultiplexing systems to a value close to minimum. Implementation advantages of that technique are pointed out. The highest efficiency is achieved when the number of channels is close to a power of 2, which is demonstrated by the '60-channel frequency-division-multiplexing (FDM)-2 X 30-channel time- division-multiplexing (TDM) transmultiplexer; a rough estimate of the computation rate is carried out in a practical case and appears to be quite within reach of the present technological capabilities. Significant cost advantage over equivalent analog equipment is expected. A digital version of the 12-channel FDM system using the same technique is also considered.

Fast-Fourier-Transform Spectral-Analysis Techniques as a Plasma Fluctuation Diagnostic Tool

Abstract: A review is given of the key ideas involved in computing power spectral density functions from fast-Fourier-transformed plasma fluctuation data. Next a model is described which enables one to determine, from the computer-generated power spectra, the amplitude, frequency, and wavenumber of each of several waves present in the plasma. The potential of digitally implemented spectral analysis techniques as a plasma diagnostic tool is demonstrated in an experimental study of the evolution, and ultimate turbulent destruction, of a multi-mode drift wave spectrum.

Identification of the Modal Properties of an Elastic Structure From Measured Transfer Function Data

Abstract: A technique for identifying the modal properties of an elastic structure in a testing laboratory is presented. The technique is based upon the use of digital processing and the fast Fourier transform (FFT) to obtain transfer function data, and then the use of a least squared error estimator t o identify modal properties from the transfer function data. Both analytical and experimental results are presented.

Fast fourier transform stage using floating point numbers

Abstract: System for performing complex Fourier operations of multiplying a fixed complex number by a floating point complex number and adding to the resulting product another floating point complex number.

Matrix representations for sorting and the fast Fourier transform

Abstract: The different versions of the fast Fourier transform (FFT) are described here for arbitrary base in terms of the matrix factors of the discrete Fourier transform matrix T_{N} . The Kronecker product notation and the ideal shuffle base r permutation operator form the basis for a unifying theory through which the various versions of the FFT can be viewed. The properties of the ideal shuffle base r permutation operator are used to arrive at FFT versions with such desirable properties as in-place computation or identical geometry from stage to stage. The FFT versions previously described in the literature are derived here. At the same time, algorithms for the sorting of FFT data in digit-reversed order are generated. These are explored and new sorting versions amenable to hardware implementation with sequential memory are presented. As an example of how the unifying theory is used, a number of FFT versions with identical geometry from stage to stage are derived. The hardware necessary for these algorithms is described for the base 4 case with N = 1024 data points.

Generation of immittance functions in symbolic form for lumped distributed active networks

Abstract: An efficient method for numerically generating the immittance and sensitivity parameters of linear time-invariant lumped distributed active networks as explicit functions of the frequency variable s is presented. It is based on the fast Fourier transform (FFT) algorithm for numerical interpolation, the sparse-matrix method for efficient computation and low storage, and the adjoint-network approach for sensitivity evaluation. The situation when a few of the network element values are to be left as symbols is considered. The influence of various numerical errors is investigated and ways of reducing them are proposed.

Spectrum of a binary signal block coded for DC suppression

Abstract: This paper analyzes a block-coding scheme designed to suppress spectral energy near f = 0 for any binary message sequence. In this scheme, the polarity of each block is either maintained or reversed, depending on which decision drives the accumulated digit sum toward zero. The polarity of the block's last digit informs the decoder as to which decision was made. Our objective is to derive the average power spectrum of the coded signal when the message is a random sequence of + 1's and −1's and the block length (M) is odd. The derivation uses a mixture of theoretical analysis and computer simulation. The theoretical analysis leads to a spectrum description in terms of a set of correlation coefficients, {p q } = q = 1, 2, etc., with the p q 's functions of M. The computer simulation uses FFT algorithms to estimate the power spectrum and autocorrelation function of the block-coded signal. From these results, {p q } is estimated for various M. A mathematical approximation to p q in terms of q and M is then found which permits a closed-form evaluation of the power spectrum. Comparisons between the final formula and simulation results indicate an accuracy of ±5 percent (±0.2 dB) or better. The block-coding scheme treated here is of particular interest because of its practical simplicity and relative efficiency. The methods used to analyze it can be applied to other block-coding schemes as well, some of which are discussed here for purposes of comparison.

A New Algorithm for Computing Correlations

Abstract: In this correspondence we present a new algorithm for computing the correlation [mi][/mi]. For applications where the "cost" of a multiplication is greater than that of an addition, the new algorithm is always more computationally efficient than direct evaluation of the correlation, and it is generally more efficient than FFT methods for processing 128 or fewer data points, or for calculating only the first L values of Rk, for L < 10 log2 2N.

Optimum Fourier-transform division filters with magnitude constraint

Abstract: Fourier-transform division filters are discussed. Using integrated squared error as a fidelity criterion with the magnitude of the filter transfer function subject to a constraint, the optimum spatial filter is developed. By consideration of the problem of image transformation, various methods for improving image reconstruction by altering image phase are discussed. The input-image phase and the desired output-image phase may be chosen to improve the performance of the filtering system. The problem is to shape the spectra of the input and the desired output. An algorithm, previously used for computing kinoforms, effectively determines an image phase that significantly improves the image reconstructed from the spatial filters.

Digital FFT processor using random access memory

Abstract: A system for digital signal processing including a random access memory accessed by counters and used for storing and shifting signals in a fast Fourier transformer (FFT).

A fast algorithm for the estimation of autocorrelation functions

Abstract: In this paper a fast algorithm for the transformation of the logical autocorrelation function to the arithmetic autocorrelation function is derived, and a computationally efficient procedure for estimating an arithmetic autocorrelation function via fast Walsh transform (FWT) techniques is described. The savings in computer time over straightforward lagged-product computations or the fast Fourier approach is considerable.

Generation of Dolph-Chebyshev weights via a fast Fourier transform

Abstract: Dolph-Chebyshev weights, which realize a minimum side-lobe level for a specified main-lobe width, can be generated by a single fast Fourier transform (FFT). For an even number of elements 2H, the size of the FFT is H. This result has utility for spectral analysis as well as for array processing.

An algorithm for performing an inverse chirp z-transform

Abstract: An efficient algorithm for the determination of the coefficients of a polynomial from evenly spaced sample values of that polynomial on a spiral contour in the complex plane is presented. It is useful for the determination of a sequence from evenly spaced values of its Fourier transform.

Roundoff error in multidimensional generalized discrete transforms

Abstract: The analysis of rounding error in the one-dimensional fast Fourier transform (FFT) is extended to a class of generalized orthogonal transforms [1] with a common fast algorithm similar to the FFT algorithm. This class includes the BInary FOurier REpresentation (BIFORE) transform (BT) [2], the complex BT (CBT) [3], and the discrete Fourier transform (DFT). Expressions for the mean square error (MSE) in the two-dimensional BT, CBT, and FFT are derived. In the case of white input data, the mean square error-to-signal ratio is derived for the multidimensional generalized transforms. The error-to-signal ratio for the one-dimensional FFT derived by Kaneko and Liu is modified with improvement. Some comparisons among BIFORE, DFT, and Haar transforms are also included. The theoretical results for the two-dimensional FFT and BIFORE have been verified experimentally. The experimental results are in good agreement with the theoretical results for lower order sequences, but deviate as the order increases due to the actual manner of rounding in the digital computer.

WT-MBA/LLL1B: a computer program for the time-domain electromagnetic response of thin-wire structures. [In FORTRAN for CDC 7600]

Abstract: This report is a user's manual for the Fortran computer code WT-MBA/LLL1B, and represents a major extension of the code TWTD. WT-MBA/LLL1B computes the currents on thin-wire structures by using a moment method solution of an electric field integral equation. Subroutines are included to compute the radiated far fields and the frequency response of the structure through a fast Fourier transform. 2 figures, 1 table.

The use of symmetry with the fast Fourier algorithm

Abstract: This paper presents an algorithm for making use of symmetry in the fast Fourier transform in a simple and general way which is applicable to nearly all space groups. This allows one to reduce storage requirements to approximately what is needed for an asymmetric unit of the electron-density function, and hence makes possible economical forward and reverse transforms of large unit cells in core.

Parallel data streams and serial arithmetic for fast Fourier transform processors

Abstract: An algorithm is presented that introduces two degrees of parallelism into the implementation of fast Fourier transform (FFT) processors. That is, both the radix of factorization and the number of arithmetic units may be selected to achieve the required processing speed. A serial vector multiplier that is ideally suited to the implementation of a general radix arithmetic unit is described. It is subsequently shown that a fast Fourier processor having an attractive cost performance ratio can be built by employing serial arithmetic in the implementation of the algorithm developed.

Internal Waves Radiated by a Moving Source. Volume 1. Analytic Simulation

Abstract: : An algorithm is derived for the efficient simulation of internal waves radiated from an object moving at constant speed in a medium of arbitrarily stratified density. The algorithm is based on a Fourier/normal-mode expansion of the linearized fluid equations in rectangular coordinates, and owes its efficiency to the Fast Fourier Transform used for numerical inversion of the analytically-derived field transforms. Sample calculations from a prototype computer program, XMODE, are described.

An Approximate Fast Fourier Transform Technique for Vernier Spectral Analysis

Abstract: : An approximate and quick fast Fourier transform technique for vernier spectral analysis is derived and tested for several candidate time-and delay- weightings, and for overlaps of the time weightings. For 50 percent overlap, the use of a simple cosine lobe for the time weighting yields spurious spectral sidelobes at least 23 dB below the main peak, whereas Dolph-Chebyshev time weighting achieves -33 dB sidelobes. For 75 percent overlap, use of a (cosine) (sup 5) lobe for the time weighting yields sibelobes at least 54 dB down, whereas Dolph-Chebyshev time weighting achieves -86 dB sidelobes. In both cases of overlap, use of delay weighting is also required and is taken as a Hanning weighting. Extensions to other overlaps and weightings are possible from the fundamental relations presented and from the sample program furnished.

An Analysis of Mathematical Transformations and a Comparison of Numerical Techniques for Computation of High-Energy CW Laser Propagation in an Inhomogeneous Medium

Abstract: : Present methods for modeling the propagation of focused and collimated laser beams are examined. Methods used for transforming the paraxial equation into a form more suitable for computation are generalized. This generalization is shown to lead to more beneficial computational characteristics than transformations previously employed. Various strategies arising from these transformations are analyzed and compared for numerical efficiency. The transformed equations are shown to be a convenient point of departure for solution by a class of numerical methods. The formulation is shown to lead to a Fast Fourier Transform (FFT) solution that does not require a Nyquist accuracy criterion, allowing the numerical procedure to march the solution forward in a more economical fashion.

Interactive analysis and display of the electroencephalogram (EEG) in real time

Abstract: The development of fast, relatively inexpensive graphics terminals permits the integration of interactive display with on-line, real time signal analysis in dedicated minicomputer systems. Interactive display in the context of electroencephalogram (EEG) analysis includes: 1. control over form and parameters of an isometric plot using hidden line suppression and floating level; 2. selection of function and transform to graph; and 3. expansion or contraction of coordinate axes and time scale, from "wide angle" views of the course of several hours of recording of the entire scalp, to "telescopic" blow-ups of the details of two or three seconds of activity in a single channel.The analysis paradigms function on-line and in real time, and incorporate parallel time domain and spectral analysis on data from eight or fewer electrode placements. Spectral estimates of power and simple coherences are typically formed using ensemble averages of non-overlapping one-half to two second periodograms obtained by Fast Fourier Transform. Transient analysis uses heuristic strategies to isolate clinically significant patterns, such as the sharp paroxysmal wave forms associated with the epilepsies. Instrumental and extra-cerebral artifacts are partially eliminated by algorithms based upon heuristic criteria. Parameters of spectral and transient analysis are interactively alterable to facilitate varying experimental paradigms.To implement such systems, which can be both compute and I/0 bound, it is necessary to optimize systems software. A simple and multitasking executive coordinates program task modules. Memory space and computing time are conserved through extensive use of dynamic buffer allocation and double precision integer arithmetic.

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions

Abstract: Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations