Showing papers on "Discrete-time Fourier transform published in 1973"
TL;DR: In this paper, a method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented, which utilizes the weighted overlapped segmentation fast Fourier transform approach.
Abstract: A method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented. The estimation technique utilizes the weighted overlapped segmentation fast Fourier transform approach. Analytical and empirical results for statistics of the estimator are presented. The analytical expressions are limited to the nonoverlapped case; empirical results show a decrease in bias and variance of the estimator with increasing overlap and suggest a 50-percent overlap as being highly desirable when cosine (Hanning) weighting is used.
521 citations
01 Oct 1973
TL;DR: The smoothed coherence transform is defined and examples of its uses and shortcomings are given and Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
Abstract: The smoothed coherence transform (SCOT) is defined and examples of its uses and shortcomings are given. Computation of this function shows promise for measuring time delays between weak broad-band correlated noises received at two sensors.
203 citations
TL;DR: Methods for incorporating crystallographic symmetry properties into complex Fourier transforms in a form particularly well suited for use with the Cooley-Tukey fast Fourier transform algorithm are presented.
Abstract: This paper presents methods for incorporating crystallographic symmetry properties into complex Fourier transforms in a form particularly well suited for use with the Cooley-Tukey fast Fourier transform algorithm. The crystallographic transforms are expressed in terms of a small number of one-dimensional special cases. The algebra presented here has been used to write computer programs for both Fourier syntheses and Fourier inversions. Even for some quite large problems (7000 structure factors and 149000 grid points in the asymmetric unit) the rate-limiting step is output of the answers.
199 citations
TL;DR: The theoretical basis for representation of a speech signal by its short-time Fourier transform is discussed and the design tradeoffs necessary to achieve moderate information rate reductions are elucidated.
Abstract: This paper discusses the theoretical basis for representation of a speech signal by its short-time Fourier transform. The results of the theoretical studies were used to design a speech analysis-synthesis system which was simulated on a general-purpose laboratory digital computer system. The simulation uses the fast Fourier transform in the analysis stage and specially designed finite duration impulse response filters in the synthesis stage. The results of both the theoretical and computational studies lead to an understanding of the effect of several design parameters and elucidate the design tradeoffs necessary to achieve moderate information rate reductions.
116 citations
TL;DR: 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.
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.
115 citations
TL;DR: In this article, the Fourier transform of the spin echo using the pulsed gradient, spin echo technique was used to determine the self-diffusion coefficient of each component in a multicomponent system.
115 citations
107 citations
TL;DR: The fast Fourier transform is employed in the most efficient measurement of the Wiener kernels of a non-linear system so far discovered.
Abstract: A new method is presented for the measurement of the Wiener kernels of a non-linear system. The method uses the complex exponential functions as a set of orthogonal functions with which to expand the kernels. The fast Fourier transform is then employed in the most efficient measurement of the kernels so far discovered.
105 citations
TL;DR: In this article, it was shown that the truncation error can also be removed at discrete frequencies, simply by first subtracting a ramp from the step response of a network, with consequent noise enhancement.
Abstract: If the discrete Fourier transform of the step response of a network is taken, a large truncation error results, since only a finite number of samples is used. This error is usually removed by first differentiating the waveform, with consequent noise enhancement. The letter shows that the error may also be removed at discrete frequencies, simply by first subtracting a ramp from the step response.
TL;DR: In this paper, Fourier transform and their physical applications are discussed in the context of Optica Acta and International Journal of Optics: Vol. 20, No. 11, pp. 915-915.
Abstract: (1973). Fourier Transforms and Their Physical Applications. Optica Acta: International Journal of Optics: Vol. 20, No. 11, pp. 915-915.
TL;DR: In this paper, the Fast Fourier Transform (FFT) is used for fitting experimental data described by a sum of exponentials, which has been shown to be well suited for use even on a small computer.
Patent•
30 Jul 1973TL;DR: In this paper, a coherent beam of light is modulated by signals from an array of hydrophones, which are processed in a sequence that includes optical Fourier transform and re-mapping operations that conserve phase and amplitude.
Abstract: A coherent beam of light is modulated by signals from an array of hydrophones. Multi-dimensional optical Fourier transform processing is accomplished in a sequence that includes optical Fourier transform and re-mapping operations that conserve phase and amplitude. In such optical processing of signals from the array the first or temporal Fourier plane of multichannel frequency analysis is scanned to perform a sequence of one or two-dimensional spatial transforms. The spatial transforms, each of which corresponds to a discrete acoustic frequency, are performed after re-mapping the frequency analyzed data into an optical space model of the acoustic array. The means for remapping the data is a set of dielectric wave guides. Alternatively, optical signals are physically measured and then re-mapped.
Patent•
01 Oct 1973TL;DR: In this paper, a discrete frequency domain equalization system was proposed for high-speed synchronous data transmission systems, where, in a preferred embodiment, samples of an input signal in the time domain are transformed by a discrete fast Fourier transform device into samples in the frequency domain.
Abstract: A discrete frequency domain equalization system is disclosed for utilization in a high-speed synchronous data transmission system where, in a preferred embodiment, samples of an input signal in the time domain are transformed by a discrete fast Fourier transform device into samples in the frequency domain. Reciprocal values of these frequency domain samples are derived from a reciprocal circuit and then transformed by an inverse discrete fast Fourier transform device into time domain samples which are the desired tap gains that are applied to a transversal equalizer in order to minimize the errors in a received signal caused by intersymbol interference and noise.
IBM1
TL;DR: Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
Abstract: A solution is given to the problem of deconvolving two time sequences using discrete Fourier transform (DFT) techniques when one of the sequences is of infinite duration. Both input- and impulse-response deconvolution problems are considered. Results are summarized of a computer study of the algorithm that performs the deconvolution iteratively, using the fast Fourier transform (FFT) algorithm at each stage.
TL;DR: In this paper, a non-recursive transform equation for the Fourier transform of a discrete Walsh function with a rectangular pulse was developed, which is a function of the bits of the Gray code number for the order of the Walsh function.
Abstract: Convolution of a discrete Walsh function with a rectangular pulse simplifies the derivation of an expression for the Fourier transform of a Walsh function. The nonrecursive transform equation that is developed is a function of the bits of the Gray code number for the order of the Walsh function.
01 Nov 1973
TL;DR: Askey as mentioned in this paper showed that the Fourier transform of an even function which is convex for x = or > 0, continuous and vanishes at infinity is nonnegative and pointed out that this transform could be inverted, so that the function is positive definite and if it is one when x is zero, it is a characteristic function.
Abstract: : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTERRadial Characteristics Functions.Technical summary rept.,SAskey,Richard ;MRC-TSR-1262DA-31-124-ARO(D)-462*Fourier transformation, Measure theory, Bessel functions, TheoremsPolya theorem, *Characteristic functionsIn 1918 Polya proved that the Fourier transform of an even function which is convex for x = or > 0, continuous and vanishes at infinity is nonnegative. In 1949 he pointed out that this transform could be inverted, so that the function is positive definite, and if it is one when x is zero, it is a characteristic function. An extension of this result to n-dimensions is presented. (Modified author abstract)
TL;DR: The geophysicist involved in the analysis ofTwo-dimensional data should have an understanding of the two-dimensional finite Fourier transform and the mechanics of two- dimensional filtering.
Abstract: The geophysicist involved in the analysis of two-dimensional data should have an understanding of the two-dimensional finite Fourier transform and the mechanics of two-dimensional filtering. Frequency aliasing must be considered when working with sampled data. In two dimensions it is advantageous to consider aliasing in terms of the overlap of the repeating spectra inherent in the finite Fourier transform. Two-dimensional filtering can be performed as a transient convolution in the space domain, as cyclic convolution utilizing the frequency domain or as the multiplication of polynomials using the z-transform. If the “edge” effects are removed, the results of the three methods are identical.
TL;DR: It is shown how simple integration rules can be associated with the Fast Fourier Transform technique in order to obtain accurate results without reducing essentially the speed of computation.
Patent•
18 Apr 1973
TL;DR: In this paper, an input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the input by a successively larger time delay.
Abstract: An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. Given the separated frequency components, the original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
TL;DR: The Damped Fourier Spectrum (D.F.S) as mentioned in this paper represents a new way of smoothing the classical Fourier Transform by using a physically based filter, and it can be represented by a linear combination of the real and imaginary parts of the spectrum.
Abstract: This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the “Damped Fourier Spectrum” (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial conditions. The D.F.S. represents a new way of “smoothing” the classical Fourier Transform by using a physically based filter.
01 Nov 1973
TL;DR: In this paper, an optimal phase demodulator is realized by sequentially calculating the Fourier coefficients of the conditional density of the phase and phase rate given the observations, and the point mass method of carrying the density and its resultant estimate is shown to be the same as that of a Fourier filter.
Abstract: : An optimal phase demodulator is realized by sequentially calculating the Fourier coefficients of the conditional density of the phase and phase rate given the observations. The point mass method of carrying the density and its resultant estimate is shown to be the same as that of the Fourier filter. The advantage of the Fourier filter is that it produces estimates eight times faster than the point mass filter while retaining fidelity. (Author)
TL;DR: If an N -sample time signal is to contain a fraction of its energy in T consecutive samples, then the minimum number of frequency components containing that same energy fraction must be greater than N/T(2\gamma - 1)^2.
Abstract: We study the form assumed by the classical time-frequency uncertainty relations in discrete as well as nontrigonometric spectral analysis. In particular we find that if an N -sample time signal is to contain a fraction \gamma of its energy in T consecutive samples, then the minimum number of frequency components containing that same energy fraction must be greater than N/T(2\gamma - 1)^2 . It is also found that the discrete Walsh transform permits greater energy concentration (less uncertainty) than the discrete Fourier transform.
TL;DR: In this article, the spatial variation of the light field from a random object is treated for a case with a gaussian and diverging beam illumination, and the variation on the object can be clearly described by the convolution integral of the Fourier transforms of its transmission function and the illumination function.
Abstract: The spatial variation of the light field from a random object is treated for a case with a gaussian and diverging beam illumination. It is shown that, in the reciprocal space, the variation on the object can be clearly described by the convolution integral of the Fourier transforms of its transmission function and the illumination function, and is transmitted through a linear system specified by a frequency response function (the Fourier transform of the Fresnel wave-function). The second moment of the fluctuating wavefield is given in the form of the Fourier transform, and is derived for a moving ground glass on the assumption that the glass gives a pure phase variation obeying the gaussian process. The variation in the degree of coherence is examined by taking the beam spread, the roughness and the correlation length as parameters. These results are compared with the ones obtained in the mathematical limit of the beam spread. The experimental results are shown for various beam spreads and roughnesses. The results are in good agreement with the theoretical calculations.
TL;DR: The filter bank of the pulse-Doppler radar receiver is shown to be realizable by a set of digital filters that can be obtained directly from the DFT.