Showing papers on "Discrete sine transform published in 1971"

Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform

Abstract: The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.

The fast Fourier transform in a finite field

Abstract: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the 'fast Fourier transform' algorithm. The transform may be applied to the problem of calculating convolutions of long integer sequences by means of integer arithmetic.

Computation of spectra with unequal resolution using the fast Fourier transform

Abstract: The discrete Fourier transform of a sequence, which can be computed using the fast Fourier transform algorithm, represents samples of the z transform equally spaced around the unit circle. In this letter, a technique is discussed and illustrated for transforming a sequence to a new sequence whose discrete Fourier transform is equal to samples of the z transform of the original sequence at unequally spaced angles around the unit circle.

The Design of a Class of Fast Fourier Transform Computers

Abstract: The design of a class of special-purpose computers for time-series analysis by Fourier transformation is described. The computers are sequential machines which implement machine-oriented fast Fourier transform algorithms obtained by factoring the discrete Fourier transform to an arbitrary radix.

A generalized discrete transform

Abstract: A class of discrete transforms for signal processing is defined. Elementary properties of this set of transforms are compiled and presented.

Real signals fast Fourier transform: Storage capacity and step number reduction by means of an odd discrete Fourier transform

Abstract: An odd discrete Fourier transform (ODFT) which relates in several ways to the usual discrete Fourier transform (DFT) is introduced and discussed. Its main advantage is that it can readily be applied to spectrum and correlation computations on real signals, by halving the storage capacity and greatly reducing the number of necessary steps.

Complex BIFORE transform

Abstract: Complex BIFORE (Binary FOurior REpresentation) transform belongs to the family of discrete orthogonal transformations and is analogous to discrete Fourier transform (DFT) when dealing with complex inputs. For real inputs, complex BIFORE transform (CBT) reduces to BIFORE or Hadamard transform (BT or HT) whose bases are Walsh functions. BT has been applied in several phases of information processing and sequency filters and sequency multiplexing equipment have also been built. When dealing with complex signals, CBT has some inherent computational advantages, and can be used to analyse and synthesize complex input functions. In the present paper, CBT is defined and its relationship to BT is shown. Several properties of CBT are developed. Invariance of power spectrum to sequential shift of the sampled data is shown. Using matrix factoring, fast algorithms suitable for digital computation of CBT and its inverse are developed. CBT is extended to multiple dimensions. Fast algorithms and corresponding fl...

The Fourier transform of spline-function approximations to continuous data

Abstract: The transform of a spline-function approximation to continuous data is called a spline transform. In this correspondence, the spline and the discrete Fourier transforms (DFT) are compared as means for numerical computation of the Fourier integral transform. It is shown how the spline transform reduces errors introduced by the discrete transform and alleviates noise problems when the sampling rate is limited due to experimental method or hardware constraints.

A Generalization of Harmonic Analysis for Detection of Long-Period Biorhythmicities from Short Records,

Abstract: : Successive ordinates of the line spectrum as computed by means of the discrete Fourier transform indicate how the variance of a given time series is apportioned among the members of a set of orthogonal, i.e. harmonic, frequencies. The continuous Fourier transform provides a means of interpolation between these frequencies. However, when the original data include a long-period sinusoid whose frequency is below the fundamental, then neither the discrete nor the continuous Fourier transform gives a good indication of the presence of long-period wave function. The detection and estimation of such a function can be accomplished by a generalization of harmonic analysis along the framework of regression analysis. The procedure computes a squared multiple correlation coefficient corresponding to any frequency, by regressing sine and cosine weights on the observed data. The method and its applications are illustrated by simple numerical examples. (Author)