Showing papers on "Discrete Hartley transform published in 1977"

A Fast Computational Algorithm for the Discrete Cosine Transform

Abstract: A Fast Discrete Cosine Transform algorithm has been developed which provides a factor of six improvement in computational complexity when compared to conventional Discrete Cosine Transform algorithms using the Fast Fourier Transform. The algorithm is derived in the form of matrices and illustrated by a signal-flow graph, which may be readily translated to hardware or software implementations.

A prime factor FFT algorithm using high-speed convolution

Abstract: Two recently developed ideas, the conversion of a discrete Fourier transform (DFT) to convolution and the implementation of short convolutions with a minimum of multiplications, are combined to give efficient algorithms for long transforms Three transform algorithms are compared in terms of the number of multiplications and additions Timing for a prime factor fast Fourier transform (FFT) algorithm using high-speed convolution, which was programmed for an IBM 370 and an 8080 microprocessor, is presented

Index mappings for multidimensional formulation of the DFT and convolution

Abstract: The mapping of one-dimensional arrays into two- or higher dimensional arrays is the basis of the fast Fourier transform (FFT) algorithms and certain fast convolution schemes. This paper gives the general conditions for these mappings to be unique and cyclic, and then considers the application to discrete Fourier transform (DFT) and convolution evaluation.

Discrete Hilbert transform filtering

Abstract: A discrete filtering technique based on circular convolution is presented. The discrete Hilbert transform (DHT), in matrix form and other matrices for filtering by circular convolution, is shown to compare favorably with DFT and FFT filtering. The comparison is presented in terms of error accumulation.

On number theoretic Fourier transforms in residue class rings

Abstract: The proof of the orthogonality conditions that must be fulfilled by the transform factor α of a NTFT of length N, is based upon the possibility of cancelling all nonzero factors of the form (αq- 1), q = 1, 2,..., N - 1. In a residue ring containing zero divisors, this is not allowed, unless all such factors can be shown not to be divisors of zero. It is shown that this is the case, when a is any primitive Nth root of unity, N being an allowed transform legnth. At the same time, a property is established that helps to reduce the amount of searching needed to find suitable transform factors.

A Table of Discrete Fourier Transform Pairs

Abstract: A classification of methods for generating discrete Fourier transform pairs is given, followed by a table of 29 pairs. Many of these are new, whereas some have been collected from various literature sources. We have tried to make the table interesting rather than comprehensive. The generalization of the Gaussian sums is a good example. Hundreds of additional nonobvious finite identities can be deduced by using the Rayleigh-Parseval formula and convolutions.

Winograd's algorithm applied to number-theoretic transforms

Abstract: We show how to perform a number-theoretic transform (n.t.t.) using an algorithm analogous to that of S. Winograd for computing the discrete Fourier transform (d.f.t.). Using this algorithm, the range of data lengths and word lengths is much larger than that available with conventional fast n.t.t.s.

Properties of the Discrete Fourier Transform (DFT)

Abstract: This paper will be divided into two parts. The first is intended as a companion to a tutorial session on those basic properties of the DFT which lead to Fast Fourier Transform algorithms. The second part will range more widely, in particular considering ways in which certain less well-known properties of the DFT could be turned to practical use. The two parts are independent.

Realization of a discrete Fourier transform (DFT) module for incorporation in FFT processors

Abstract: For applications requiring high-speed and in-place treatment, it is often advantageous to realize special-purpose computers. This paper describes a discrete Fourier transform (DFT) module for incorpration in fast Fourier transform (FFT) processors. The module is highly suitable for real input applications requiring high-speed transformations. It attributes one point to all frequency channels in one clock cycle. This treatment is not only well suited for the present technology, but appears to be more attractive in view of recent trends in digital circuitry.

A linear-filtering transform algorithm based on permutations

Abstract: An algorithm is described which computes the discrete Fourier transform using only the following operations: multiplication by a term of constant frequency; multiplication by a sequence containing only the four numbers ± 1, ± j; permutation of the sequence; convolution with a fixed impulse response; permutation of the convolved sequence, multiplication by a sequence containing only ± 1, ± j, and multiplication by a term of constant frequency. Using charge-coupled devices, the fixed convolution and the multiplications by ± 1, ± j are relatively easy operations. The permutations are also believed to be reasonably easy. The multiplications by constant frequency terms can be ignored in many applications and the resulting "transform" still represents the spectrum and still has a straightforward convolution property.