Showing papers on "Hartley transform published in 1981"
TL;DR: In this article, a class of real valued, integrable functions f(x) and corresponding functions M$x) such that f (x) 1, and the value of MfO) is miimi were determined.
Abstract: We determine a class of real valued, integrable functions f(x) and corresponding functions M$x) such that f(x) 1, and the value of MfO) is miimi. Several applications of these functions to number theory and analysis are given.
76 citations
TL;DR: In this paper, a hybrid system combining the optical Mellin transform and a digital signal processing technique is discussed for scale-invariant pattern classification, in which circular or periodic correlation is employed.
34 citations
13 Jul 1981
TL;DR: A class of VLSI networks for computing the Discrete Fourier Transform and the product of two N-bit integers is presented and it is shown how to design multipliers with area A = O(N) and time T=O(√N) on one hand, and A=0((N/log2N)2), T= O(log2 N) on the other.
Abstract: In this paper we present a class of VLSI networks for computing the Discrete Fourier Transform and the product of two N-bit integers. These networks match, within a constant factor, the known theoretical lower-bound O(N2) to the area × (time)2 measure of complexity. While this paper's contribution is mainly theoretical, it points toward very practical directions: we show how to design multipliers with area A = O(N) and time T=O(√N) on one hand, and A=0((N/log2N)2), T = O(log2N) on the other. Both of these designs should be contrasted with the currently available multipliers, whose performances are A=O(N), T=O(N) or even A=O(N2), T=O(N).
33 citations
TL;DR: An integral transform which converts a real spatial (or temporal) function into a real frequency function is introduced in this paper, and the properties of this transform are investigated, and it is concluded that this transform is parallel to the Fourier transform and may be applied to all fields in which the FFT has been successfully applied.
31 citations
TL;DR: In this paper, three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples, and all three methods employ the property that the Hdbert transform is a convolution.
Abstract: Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/πx is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high-frequency components.
19 citations
TL;DR: In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets.
16 citations
TL;DR: In this article, a coherent optical Fourier transform system has been modified to compute cosine transforms optically by creating a symmetrical pattern at the input Cosine transform is known to be useful for data compression and image coding especially when the image space-bandwidth product is finite.
7 citations
TL;DR: By means of techniques with linear operators the uniqueness problem of object reconstruction and the characterization of data has been studied for the “Fourier Transform” optical system.
7 citations
01 Jan 1981
TL;DR: The X-ray transform which we studied for Rn of course makes sense for an arbitrary complete Riemannian manifold X as mentioned in this paper, which is the manifold of interest of this paper.
Abstract: The X-ray transform which we studied for Rn of course makes sense for an arbitrary complete Riemannian manifold X.
5 citations
TL;DR: The inversion and the characterization of the convolution transform is derived via the concept of unimodality introduced by Khintchine (1938) and yields simple and intuitively appealing proofs.
Abstract: Abstract The inversion and the characterization of the convolution transform is derived via the concept of unimodality introduced by Khintchine (1938). This method yields simple and intuitively appealing proofs.
4 citations
TL;DR: An algorithm for computing a complex-number theoretic transform of long sequences that can be used to perform the matched-filter correlation of raw radar-echo data and the range response function for producing images from synthetic aperture radar (SAR) data.
Abstract: This correspondence describes an algorithm for computing a complex-number theoretic transform of long sequences. Such a transform technique can be used to compute the convolution of two sequences of complex numbers. Emphasis is given to a transform of length 9.8.31 = 2232. Such a transform can be used to perform the matched-filter correlation of raw radar-echo data and the range response function for producing images from synthetic aperture radar (SAR) data.
IBM1
TL;DR: The results indicate that several power-of-2 length polynomial transform methods developed by Nussbaumer allow one to totally avoid the row-column data corner-turn commonly encountered in Fourier Transform 2D convolution methods, while also providing significantly reduced computational complexity.
Abstract: This paper examines the matrix data re-order requirements of a variety of polynomial transform 2D convolution methods which can be employed to efficiently accommodate large field problems. The results indicate that several power-of-2 length polynomial transform methods developed by Nussbaumer allow one to totally avoid the row-column data corner-turn commonly encountered in Fourier Transform 2D convolution methods, while also providing significantly reduced computational complexity. Execution time comparison with an FFT reference base is made assuming the use of general register and array processor units and use of recently developed matrix-transpose methods by Eklundh and Ari to support 2D Fourier Transform corner-turn requirements. These results demonstrate a 2-4 times throughput performance improvement for use of the polynomial transform method in place of the 2D Fourier Transform approach to circularly convolve large 2D fields in the range 1024×1024 to 8192×8192.
TL;DR: In this paper, a new technique of obtaining a complete orthonormal transform based on a particular interpretation of DFT is developed, which can be deduced from the knowledge of the permutation properties of the two component transforms.
Abstract: A new technique of obtaining a complete orthonormal transform based on a particular interpretation of DFT is developed. One such transform, namely, the Fourier-twiddled H-DF transform, has been discussed in detail. The permutation properties of such transforms can be deduced from the knowledge of the permutation properties of the two component transforms.
01 Jan 1981
TL;DR: The average running time for several FFT algorithms is analyzed and examples are given to show that padding by zeros to the nearest power of 2 can lead to real distortions.
Abstract: The average running time for several FFT algorithms is analyzed. The Cooley-Tukey algorithm is shown to require about n1.61 operations. The chirp algorithm always works in 0(n log n) operations. Examples are given to show that padding by zeros to the nearest power of 2 can lead to real distortions.