Showing papers on "Discrete-time Fourier transform published in 1993"

A simple algorithm for fitting measured data to Fourier‐series models

Abstract: An algorithm is described for fitting measured data to Fourier‐series models of any order without recourse to discrete Fourier transform or curve‐fitting routines. The implementation of this algorithm requires only simple basic mathematical operations and can be easily implemented in microcomputer‐ or microprocessor‐based real‐time systems.

An efficient recursive algorithm for time-varying Fourier transform

Abstract: An efficient recursive algorithm for computing the time-varying Fourier transform (TVFT) or short-time Fourier transform (STFT) of a time sequence is presented. In this approach, instead of excluding the old samples, their importance is diminished by using all-pole moving windows. This recursive algorithm requires about one half of the computation and storage of the Amin's algorithm. The resulting TVFT does not possess any sidelobes. The performance of the algorithm is illustrated by two numerical examples. >

Hexagonal fast Fourier transform with rectangular output

Abstract: Hexagonal sampling is the most efficient sampling pattern for a two-dimensional circularly bandlimited function. A separable fast discrete Fourier transform (DFT) algorithm for hexagonally sampled data that directly computes output points on a rectangular lattice is reported. No interpolation is required. The algorithm has computational complexity comparable to that of standard two-dimensional fast Fourier transforms. >

Method of removing spurious responses from optical joint transform correlators

Abstract: A joint transform optical correlator is disclosed having an optical path length adjustment technique for causing a first optical path length between the reference image plane and the first Fourier transform lens to differ from a second optical path length between the input image plane and the first Fourier transform lens by an amount whereby the second Fourier transform lens separates the desired cross-correlation signals from the undesired signals to enhance the performance and reliability of the correlator.

Coherent signal power detector using higher-order statistics

Abstract: A signal detection system divides a data sampling run into blocks and perms a fast Fourier transform on each block, sorting results by frequency. Combinations of results of the fast Fourier transform corresponding to each frequency are processed to derive a test statistic which is unbiased by Gaussian noise while including such combinations of results of the fast Fourier transform which would be redundant over other combinations. Information concerning the frequency behavior of the signal derived in the course of detection, is accomplished with increased sensitivity.

A new systolic realization for the discrete Fourier transform

Abstract: A systolic array for the discrete Fourier transform (DFT) is proposed. In comparison with previous schemes, the proposed scheme reduces the number of multipliers required almost by half and thus saves a considerable amount of hardware. >

Signals And Filters

Abstract: Intended for a two-semester course. Chapters discuss linear, time invariant, continuous-time systems and discrete-time systems; the Fourier transform; the Laplace transform; analog filters; the discrete Fourier transform; the z-transform; and digital filters. Worked examples and exercises are includ

Spectral analysis of cervical cells using the discrete Fourier transform.

Abstract: This paper contains results from a preliminary study of spectral analysis techniques applied to the classification of cervical cells from routinely prepared Papanicolaou cervical smears. Experiments were conducted using a subset of 110 normals and 110 dyskaryotic single cell images randomly selected from a larger cell image data base. An assessment was made of the contribution of different regions within a cell image to the frequency spectrum. Three image sets were used, the original image itself plus two derived from it. In the first derived set, only nuclear size and shape were used. In the second set nuclear morphology and texture were included. Nuclear masking was performed using an interactive segmentation procedure. The discrete Fourier transform was applied to each image in the three image sets and classification experiments were performed using 80 features derived from the frequency spectra. An optimum set of features was selected for each experiment by canonical analysis. Good classification results were obtained when features extracted solely from nuclear shape were used. The inclusion of information relating to nuclear texture improved the results. However, inclusion of the extra nuclear region degraded the classifier's ability to discriminate between cell groups.

Efficient computation of the time-domain scattering from bodies of revolution

Abstract: An approach obtaining the time-domain scattering from metal, dielectric, or dielectric-coated bodies of revolution (BORs) is presented. The axial symmetry of the BORs enables a Fourier mode decomposition in the frequency domain, thereby allowing three-dimensional problems to be treated in two dimensions. By implementing the moment method and inverse discrete Fourier transform techniques, the proposed approach enables the time-domain analysis of more complicated objects, such as multiple metal scatterers and dielectric-coated scatterers. The effects of lossy and dispersive materials can be easily included in the time-domain analysis. Several examples are presented to illustrate the capabilities of the proposed approach. >

The poorman's transform: approximating the Fourier transform without multiplication

Abstract: A time-domain to frequency-domain transformation for sampled signals which is computed with only additions and trivial complex multiplications is described. This poorman's transform is an approximation to the usual Fourier transform, obtained by quantizing the Fourier coefficients to the four values (+or-1, +or-j), and is especially useful when multiplication is expensive. For the general case of an N-point quantization, an analytic formula is given for the error in the approximation, which involves only contributions from aliased harmonics. Continuous-time signals are considered; in this case the approximation is exact for bandlimited signals. >

Generalized Fourier-grid R-matrix theory; a discrete Fourier-Riccati-Bessel transform approach

Abstract: The authors present the latest developments in the Fourier-grid R-matrix theory of scattering These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform They apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation As this technique is quite new, they have hopes to broaden the formalism to many types of problems

Evolutionary spectral estimation based on adaptive use of weighted norms

Abstract: In this paper, an evolutionary spectral estimator based on the application of Adaptive Weighted Norm Extrapolation (AWNE) is formulated and illustrated for analysis of nonstationary signals. The AWNE method produces a stationary extension of the data so that computing its Fourier transform yields a nonparametric, high-resolution spectrum estimate. The evolutionary formulation described here uses a time slice of the time-averaged Spectrogram to select the initial weight function (prior spectrum) used in AWNE for each block of data. This function strongly influences the final shape of the resulting spectrum. The resulting Short-Time AWNE (STAWNE) time-frequency representation yields improved frequency-domain resolution, preserves components which last longer than one time block, and is devoid of cross-terms. Comparison with short-time autoregressive spectral estimation yields improved consistency in the spectral energy levels as time varies. Finally, this sequential spectrum estimator is also illustrated for use in range-Doppler imaging of reflectivity surfaces having prominent scatterers by hybrid two-dimensional spectral estimation in-tandem with the discrete Fourier transform.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Two-dimensional image reconstruction from Fourier coefficients computed directly from zero crossings

Abstract: Two-dimensional image reconstruction using Fourier coefficients that are computed directly from the sampled representation of zero crossings is demonstrated. A two-dimensional image of dimensions Nx × Ny is interpreted as a set of Ny independent x-space lines (in gray-scale format) that are arranged uniquely along the y direction. Each line has Nx elements. Reconstruction is achieved first by computing the entire set of Ny one-dimensional Fourier transforms from the measured zero crossings using Newton’s formula. Each Nyth line spectra has Nx Fourier coefficients. The inverse Fourier transform is then applied to each of the line spectra to obtain a set of Ny reconstructed x-space lines. The reconstructed image is obtained by arranging the reconstructed lines properly along the y direction.

Audio signal frequency analysis method - using window functions to provide sample signal blocks subjected to Fourier analysis to obtain respective coefficients.

Abstract: The frequency analysis method involves dividing an input signal, represented by discrete sample values, into overlapping blocks using a window function and subjecting them to a Fourier transformation, to obtain a set of coefficients. Each input signal block is evaluated via a set of differing symmetrical window functions of equal length, their Fourier transformations having different bandwidths. The simultaneously generated blocks are used to provide a set of characteristic Fourier transformations, with a coefficient provided for each block, dependent on the window function Fourier transformation bandwidth. The selected coefficients have frequency bands which are only slightly overlapping, or only slightly spaced apart. USE/ADVANTAGE - Accurate simulation of human hearing characteristics. At least first five spectral coefficients processed together, e.g. in fast fourier transformation.

Efficient implementation of the Fourier dual reciprocity boundary element method using two-dimensional fast Fourier transforms

Abstract: The Poisson equation is one of the field equations which arises often in aerospace applications, and its efficient solution is of great importance to aerodynamic studies. The boundary element method (BEM) is a powerful method for the solution of such field problems as it reduces the dimension of the problem by one and leads to boundary only discretization for linear problems without distributed source/sink terms. The Fourier Dual Reciprocity Boundary Element Method (FDRBEM) was developed to retain the boundary only discretization character of the BEM. The basis of the method is the expansion of the generation term in a two-dimensional Fourier series which is in turn used to transform the BEM area integrals into contour integrals. In this paper, a two-dimensional Fast Fourier Transform (FFT) algorithm is developed to efficiently and accurately extract the Fourier coefficients of the two-dimensional series expansion of the source term. Practical concerns in the implementation of the FDRBEM are discussed. Four numerical examples are presented to validate the approach.

Quasi-synchronous sampling algorithm and its applications II High accurate spectrum analysis of periodic signal

Abstract: For Pt. I, see ibid., pp. 88-93 (1993). As one of the applications of the quasi-synchronous algorithm, a method to improve the spectrum analysis of periodic signals is described. Consisting of a quasi-synchronous window whose DTFT (discrete-time Fourier transform) has as small side-lobes as desired to reduce long-range leakage, and a compensation algorithm to reduce short-range leakage after the normal fast Fourier transform, this method will give much more accurate results of the amplitudes as well as the phases than the conventional method, especially for higher frequency components, when there exists an undesirable asynchronous deviation. This technique is also suited to analyzing multiple frequency signals and signals containing interharmonics. The only constraint is that the minimum frequency interval between two adjacent components of the signal should be wider than the window's resolution. >

Dynamic range enhancement of Fourier transform infrared spectrum measurement using delta sigma modulation.

Abstract: A method for reconstructing a spectrum from a binary interferogram observed with an Fourier transform IR spectrometer is described. With this method an interferogram is quantized with a 1-bit analog-to-digital converter with a differentiator and an integrator. This method, called delta sigma modulation, features an oversampling of a signal at a rate much higher than the Nyquist sampling rate. We show experimental examples of IR spectra reconstructed by the method, which demonstrate the potential applications of the method to Fourier transform IR analysis. The results imply that the method may exceed the dynamic range over the one attainable with a conventional Fourier transform spectrometer with an analog-to-digital converter of a finite bit number.

Using an improved procedure of fast discrete Fourier transform to analyse Mössbauer spectra hyperfine parameters

Abstract: In this paper, the authors propose to supplement the mathematical processing of Mossbauer spectra (MS) by means of Fourier transforms using a regular algorithm with an iteration refinement method. The use of a priori information concerning the solution in the form of the condition of its nonnegativity allows to increase the resolution in the spectrum without the appearance of oscillations characteristic of the solutions obtained by the Fourier transform method alone. The MS of Fe-Si alloys of low concentration were processed according to the given computational scheme to evaluate the influence of the II and III coordination shells on the parameters of the hyperfine interaction on the Fe nucleus.

2 – Fourier analysis

Abstract: Publisher Summary This chapter discusses Fourier analysis and associated transform methods for both discrete-time and continuous-time signals and system. Fourier methods are based on using real or complex sinusoids as basic functions, and they allow signals to be represented in terms of sums of sinusoidal components. In order for a digital computer to manipulate a signal, the signal must be sampled at a chosen sampling rate, 1/TS, giving rise to a set of numbers called a sequence. Special analysis and many other applications often require discrete Fourier transforms (DFTs) to be performed on data sequences in real time and on contiguous sets of input samples. The theory of discrete-time, linear, time invariant systems forms the basis for digital signal processing, and a discrete-time system performs an operation on the input signal according to defined criteria to produce a modified output signal. The z-transform of the sum of two sequences multiplied by arbitrary constants is the sum of the z-transforms of the individual sequences, where Z represents the z transform operator. Data windows are introduced to smooth out the ripples introduced by the rectangular window.

A Spectral Paley-Wiener Theorem.

Abstract: The Fourier inversion formula in polar form is\(f(x) = \int_0^\infty {P_\lambda } f(x)d\lambda \) for suitable functionsf on ℝn, wherePλf(x) is given by convolution off with a multiple of the usual spherical function associated with the Euclidean motion group. In this form, Fourier inversion is essentially a statement of the spectral theorem for the Laplacian and the key question is: how are the properties off andPλf related? This paper provides a Paley-Wiener theorem within this avenue of thought generalizing a result due to Strichartz and provides a spectral reformulation of a Paley-Wiener theorem for the Fourier transform due to Helgason. As an application we prove support theorems for certain functions of the Laplacian.

Accurate determination of frequency and angle of arrival from undersampled signals

Abstract: The problem of determining the frequency and angle of arrival of an unknown signal that is undersampled when incident on a linear array is considered. A simple technique to deal with the ambiguities arising from undersampling is coupled with classic monopulse techniques to provide excellent accuracy, even in the presence of noise. Excellent results were obtained in a computer simulation. Sampling was done at 465.45 MHz and 568.88 MHz with a 512 point discrete Fourier transform. >

Electromagnetic analysis of complex microstrip structures using a CG-FFT scheme

Abstract: This work presents the extensions required in a Conjugate Gradient Fast Fourier Transform (CG-FFT) scheme to obtain scattering parameters of arbitrary geometry planar microstrip structures directly from the equivalent currents. These extensions imply the development of an appropriate method to fed and load the system. A new set of basis functions which improves the speed of convergence is also introduced. Besides, almost all computations are performed in the spectral domain where operators have simpler forms. Results are compared with measurements. The method is accurate and efficient from a computational point of view.

Determination of sampling points for nearly DFT-equivalent almost-periodic fourier transforms

Abstract: This paper presents analytical formulas for choosing sampling points required for almost-periodic Fourier transforms (APFT) of waveforms for the case of two fundamental frequencies. The generated sampling points are such that the resulting APFT is an optimal approximation of a corresponding two-dimensional discrete Fourier transform with respect to phase error, resulting in a numerically well conditioned transformation. The formulas may easily be implemented into existing APFT-based software packages.