Showing papers on "Discrete sine transform published in 1969"
01 Jan 1969
TL;DR: A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed, which provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
Abstract: The introduction of the fast Fourier transform algorithm has led to the development of the Fourier transform image coding technique whereby the two-dimensional Fourier transform of an image is transmitted over a channel rather than the image itself. This devlopement has further led to a related image coding technique in which an image is transformed by a Hadamard matrix operator. The Hadamard matrix is a square array of plus and minus ones whose rows and columns are orthogonal to one another. A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed. Since only real number additions and subtractions are required with the Hadamard transform, an order of magnitude speed advantage is possible compared to the complex number Fourier transform. Transmitting the Hadamard transform of an image rather than the spatial representation of the image provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
634 citations
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Abstract: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.
534 citations
TL;DR: An efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.
Abstract: The discrete, orthogonal Walsh functions can be generated by a multiplicative iteration equation. Using this iteration equation, an efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.
172 citations
01 Jan 1969
TL;DR: This chapter contains sections titled: Introduction, An Algorithm Suggested by Chirp Filtering, and An Algorithm Suggested By ChirP Filtering.
Abstract: This chapter contains sections titled: Introduction, An Algorithm Suggested by Chirp Filtering
121 citations
01 Jan 1969
TL;DR: In this paper, the Hilbert transform relations, as they apply to sequences and their z-transforms, and also as the number of data samples taken in the Discrete Fourier Transforms becomes infinite, are discussed.
Abstract: The Hilbert transform has traditionally played an important part in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform plays a similar role in digital signal processing. In this paper, the Hilbert transform relations, as they apply to sequences and their z-transforms, and also as they apply to sequences and their Discrete Fourier Transforms, will be discussed. These relations are identical only in the limit as the number of data samples taken in the Discrete Fourier Transforms becomes infinite. The implementation of the Hilbert transform operation as applied to sequences usually takes the form of digital linear networks with constant coefficients, either recursive or non-recursive, which approximate an all-pass network with 90° phase shift, or two-output digital networks which have a 90° phase difference over a wide range of frequencies. Means of implementing such phase shifting and phase splitting networks are presented.
77 citations
13 Oct 1969
TL;DR: A data transmission system in which the transmitted signal is the Fourier transform of the original data sequence and the demodulator is a discrete Fourier transformer, and it is shown, via computer simulation and computation of the variances of errors, how the system corrects linear channel distortion.
Abstract: The development of rapid algorithms for computation of the discrete Fourier transform has encouraged the use of this transform in the design of communication systems. Here we describe and analyze a data transmission system in which the transmitted signal is the Fourier transform of the original data sequence and the demodulator is a discrete Fourier transformer. This system is a realization of the frequency division multiplexing strategy known as “parallel data transmission”, and it is constructed in this manner so that the data demodulator, after analog to digital conversion, may be a computer program employing one of the fast Fourier transform algorithms. The system appears attractive in that it may be entirely implemented by digital circuitry. We study the performance of this system in the presence of typical linear channel characteristics. It is shown, via computer simulation and computation of the variances of errors, how the system corrects linear channel distortion.
59 citations
Patent•
22 Oct 1969TL;DR: In making a record of the exact Fourier transform of an array of beams of electromagnetic radiation, the phase of each of a substantial fraction of the beams is shifted by a constant amount before recording the transform as discussed by the authors.
Abstract: In making a record of the exact Fourier transform of an array of beams of electromagnetic radiation, the phase of each of a substantial fraction of the beams is shifted by a constant amount before recording the transform.
33 citations
TL;DR: The transform presented in this paper applies to functions which describe logic network behavior, and both form and development of this transform pair resembles the Fourier transform in harmonic analysis.
Abstract: The transform presented in this paper applies to functions which describe logic network behavior. Given a function G defined over a finite domain, it is shown that G(u) = Et F(t)ut for each element u in the domain, where finite-field arithmetic is assumed. Here, function F is the transform of G, and it is shown that F(t) = Eu G(u)(-u)-t for each integer t in a finite set. Both form and development of this transform pair resembles the Fourier transform in harmonic analysis.
28 citations
01 Jan 1969
TL;DR: Discrete Fourier transform method for factoring spectral density functions, calculating absolute error as discussed by the authors, is used to calculate absolute error of spectral density function, which is a function of spectral distribution.
Abstract: Discrete Fourier transform method for factoring spectral density functions, calculating absolute error
10 citations
TL;DR: In this paper, a general isotropic scattering kernel is considered first and is followed by the consideration of two simple kernels for the analysis of wave propagation in non-crystalline and crystalline moderators.
9 citations
TL;DR: In this article, certain striking similarities between the discrete characterisation of continuous signals by periodic sampling and by the Poisson transform are revealed, and they are used to compare the two methods.
Abstract: Certain striking similarities between the discrete characterisation of continuous signals by periodic sampling and by the Poisson transform are revealed here.
TL;DR: A fast method of generating bit-reversed addresses for the fast Fourier transform is described and it is shown that this method can be very fast and efficient.
Abstract: A fast method of generating bit-reversed addresses for the fast Fourier transform is described.
TL;DR: A technique for application of the popular fast Fourier transform (FFT) to the system identification problem and an iterative technique is discussed to avoid problems due to the circular nature of convolutions computed by the discrete Fouriertransform (DFT).
Abstract: A technique for application of the popular fast Fourier transform (FFT) to the system identification problem is outlined. Smoothing is obtained inherently in the transform and additionally by redundancy in the data. An iterative technique is discussed for the case of nonzero initial conditions and to avoid problems due to the circular nature of convolutions computed by the discrete Fourier transform (DFT).
01 Mar 1969
TL;DR: Direct and cross power spectral density estimation of discrete data using fast Fourier transform with digital filter solution is presented in this paper, where the authors propose a method to estimate the spectral density of the data.
Abstract: Direct and cross power spectral density estimation of discrete data using fast Fourier transform with digital filter solution