Showing papers on "Hartley transform published in 1968"
01 Jan 1968
TL;DR: Several properties of the FHT are revealed, including the nature of its presence in the fast Fourier transform, in which it performs the additive operations as shown by further decomposing the product of matrices representing the FFT.
Abstract: : A discrete time transform was studied and applied to the representation and discrimination of digitized signals. The transform consists of an orthogonal (Hadamard) matrix whose elements are all ones and minus ones. To facilitate implementation, a fast Hadamard transform (FHT) has been developed requiring only NlogN rather than N squared algebraic additions. Several properties of the FHT are revealed, including the nature of its presence in the fast Fourier transform, in which it performs the additive operations as shown by further decomposing the product of matrices representing the FFT.
66 citations
Patent•
28 Oct 1968
TL;DR: In this paper, a digital computer for rapidly determining the Fourier transform of a real input signal is disclosed, and the computer utilizes the symmetries of sinusoidal functions to reduce the computations required to determine a Fourier Transform.
Abstract: A digital computer for rapidly determining the Fourier transform of a real input signal is disclosed. The computer utilizes the symmetries of sinusoidal functions to reduce the computations required to determine the Fourier transform. Simultaneous addition, multiplication and memory accessing are performed by the computer thereby reducing the time normally required to compute a Fourier transform.
21 citations
12 citations
8 citations
CERN1
TL;DR: In this paper, the Fourier transform of a polynomially bounded function is expressed as a finite linear combination of analytic delta functionals applied to a continuous function on the real line in an improper sense.
Abstract: The Fourier transform of a product of two functions onSL(2,C) is expressed as a convolution integral of the Fourier transforms of its factors. With the help of this convolution integral we present the Fourier transform of a polynomially bounded function as a finite linear combination of analytic delta functionals applied to a continuous function on the real line in an improper sense.
7 citations
4 citations
TL;DR: For a simple evaluation of the Hilbert transform, iterated Fourier- or Laplace-transform schemes have been suggested as discussed by the authors, and an alternative iterated transform scheme, more general than the one previously reported, has been put forward.
Abstract: For a simple evaluation of the Hilbert transform, iterated Fourier- or Laplace-transform schemes have been suggested. In this letter, an alternative iterated transform scheme, more general than the one previously reported, has been put forward.
3 citations
2 citations
TL;DR: In this article, character recognition by Incoherent Fourier Transformation (INFT) is presented. But the method is not suitable for character recognition in the real world, as shown in Figure 1.
Abstract: (1968). Character Recognition by Incoherent Fourier Transformation. Optica Acta: International Journal of Optics: Vol. 15, No. 6, pp. 627-628.
2 citations
TL;DR: In this article, a computationally oriented transform technique for the analysis of time-varying linear systems involving both discrete-time (i.e., sampled-data) variables and continuous-time variables is presented.
Abstract: A computationally oriented transform technique for the analysis of time-varying linear systems involving both discrete-time (i.e., sampled-data) variables and continuous-time variables is presented in this paper. Finite-dimensional representations are described for the various linear operators involved, and methods for obtaining singular-value decompositions of these operators are given. The three parts of the singular-value decomposition are analogous to the direct transform, transfer function, and inverse transform of Laplace and Fourier transforms, and offer analogous insights into analysis and synthesis problems. An example is included to illustrate the analysis procedures.
TL;DR: The relation between the z transform and the transform technique introduced by Naylor is discussed and behaviour as the number of samples, N, becomes large is considered.
Abstract: The relation between the z transform and the transform technique introduced by Naylor is discussed. In particular, behaviour as the number of samples, N, becomes large ia considered.