Showing papers on "Hartley transform published in 1976"
TL;DR: The scale invariance of the Mellin transform and its optical synthesis in real-time are discussed in this article, where a scale invariant correlation and a combined Fourier-Mellin transform that is both scale and shift invariant are discussed.
Abstract: The scale invariance of the Mellin transform and its optical synthesis in real-time are discussed. An initial off-line demonstration of an optical Mellin transform is presented. A scale invariant correlation and a combined Fourier-Mellin transform that is both scale and shift invariant are discussed. Applications of these transforms in optical data processing and optical pattern recognition are emphasized.
87 citations
TL;DR: This correspondence shows that the amount of work can be cut to doing two single length FFT's, which is equivalent to doing one double length fast Fourier transform.
Abstract: Ahmed has shown that a discrete cosine transform can be implemented by doing one double length fast Fourier transform (FFT). In this correspondence, we show that the amount of work can be cut to doing two single length FFT's.
77 citations
TL;DR: Several examples are given illustrating how the Cooley–Tukey fast Fourier transform is useful as a teaching tool to introduce the subtleties of spectral analysis of sampled data by interactive minicomputer experiments.
Abstract: The Cooley–Tukey fast Fourier transform (FFT) has had an extraordinary impact on the computation of Fourier transforms. A tutorial account is given of how the algorithm works and of its relationship to the more familiar continuous Fourier transform and Fourier series. Some pitfalls associated with sampled data over a finite window are outlined. Several examples are given illustrating how the FFT is useful as a teaching tool to introduce the subtleties of spectral analysis of sampled data by interactive minicomputer experiments. A bibliography to the literature is given.
46 citations
13 citations
TL;DR: This chapter discusses application of fast Fourier transform (FFT) in radio astronomy and it is shown how this algorithm is programmed on a digital computer.
Abstract: Publisher Summary This chapter discusses application of fast Fourier transform (FFT) in radio astronomy. The Fourier transform is a particularly useful computational technique in radio astronomy. The essence of the FFT technique is that it is possible to treat the one-dimensional DFT as though it were a pseudo-two-dimensional one, and then reduce the running time by performing the inner and outer summations separately. The basic idea behind the FFT is discussed and it is shown how this algorithm is programmed on a digital computer. Because of the requirement for computational speed, a number of programs are given. These include short, moderately efficient subroutines for the transform of one-dimensional, complex data (FOURG and FOURI). With the addition of a subroutine (FXRLI) to either of the above routines, real, one-dimensional data may be transformed in half the time with half the memory storage. Additional subroutines (CFFT2, RFFT2, and HFFT2) permit the transform of two-dimensional data. A program is also given for transforming real, symmetric data for which only the cosine (or sine) transform is desired (FORSI).
12 citations
TL;DR: This correspondence develops efficient fast Fourier transform programs to transform arrays of dimension N, where N can be written as a power of two possibly multiplied by arbitrary factors.
Abstract: This correspondence develops efficient fast Fourier transform (FFT) programs to transform arrays of dimension N, where N can be written as a power of two possibly multiplied by arbitrary factors. Two programs were developed which use radix-2 and radix-4 transformations for the binary factors. These programs call another subprogram to transform with respect to the arbitrary factors, if any. Since the sequential transformation is well known, the emphasis is on developing an efficient unscrambling procedure to follow the transformation.
10 citations
01 Sep 1976
TL;DR: In this paper, a matrix formulation of the discrete Hilbert transform is presented, which has the advantage of reducing the number of multiplications by a factor of two, compared to the matrix formulation given by Burris.
Abstract: A matrix formulation of the discrete Hilbert transform, an alternative to that given by Burris [1], is presented. This has the advantage of reducing the number of multiplications by a factor of two.
8 citations
7 citations
01 Jul 1976
TL;DR: Quantization, coding, and transmission follow in order, and the reconstructed picture is produced by the two-dimensional inverse Fourier transform.
Abstract: Projection transform technique is applied to digital image transmission. Transform samples on various central sections of a Fourier space are attained with a fast Fourier transform algorithm. Quantization, coding, and transmission follow in order. The complete Fourier space information is then, upon reception of signals, estimated from the transform samples at these various central sections. The reconstructed picture is produced by the two-dimensional inverse Fourier transform.
6 citations
01 May 1976
TL;DR: Starting from the definition of the Fourier transform, the matrix expressions of both one- and two-dimensional Fourier transforms and their inverse transforms are given, which show that the discrete Fourier transformations are closely related to the nature of a balanced polyphase system.
Abstract: Starting from the definition of the Fourier transform, the matrix expressions of both one- and two-dimensional Fourier transforms and their inverse transforms are given, which show that the discrete Fourier transforms and their inverse transforms are closely related to the nature of a balanced polyphase system. The system structures are derived from the matrix expressions, which are shown diagramatically. A special feature of the system structure is that the main devices necessary for hardware implementation are tapped delay lines, product operators, adders, and a sinusoidal wave generator.
3 citations