Showing papers on "Discrete Hartley transform published in 1969"
01 Jan 1969
TL;DR: This chapter contains sections titled: Introduction, An Algorithm Suggested by Chirp Filtering, and An Algorithm Suggested By ChirP Filtering.
Abstract: This chapter contains sections titled: Introduction, An Algorithm Suggested by Chirp Filtering
121 citations
01 Jan 1969
TL;DR: In this paper, the Hilbert transform relations, as they apply to sequences and their z-transforms, and also as the number of data samples taken in the Discrete Fourier Transforms becomes infinite, are discussed.
Abstract: The Hilbert transform has traditionally played an important part in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform plays a similar role in digital signal processing. In this paper, the Hilbert transform relations, as they apply to sequences and their z-transforms, and also as they apply to sequences and their Discrete Fourier Transforms, will be discussed. These relations are identical only in the limit as the number of data samples taken in the Discrete Fourier Transforms becomes infinite. The implementation of the Hilbert transform operation as applied to sequences usually takes the form of digital linear networks with constant coefficients, either recursive or non-recursive, which approximate an all-pass network with 90° phase shift, or two-output digital networks which have a 90° phase difference over a wide range of frequencies. Means of implementing such phase shifting and phase splitting networks are presented.
77 citations
13 Oct 1969
TL;DR: A data transmission system in which the transmitted signal is the Fourier transform of the original data sequence and the demodulator is a discrete Fourier transformer, and it is shown, via computer simulation and computation of the variances of errors, how the system corrects linear channel distortion.
Abstract: The development of rapid algorithms for computation of the discrete Fourier transform has encouraged the use of this transform in the design of communication systems. Here we describe and analyze a data transmission system in which the transmitted signal is the Fourier transform of the original data sequence and the demodulator is a discrete Fourier transformer. This system is a realization of the frequency division multiplexing strategy known as “parallel data transmission”, and it is constructed in this manner so that the data demodulator, after analog to digital conversion, may be a computer program employing one of the fast Fourier transform algorithms. The system appears attractive in that it may be entirely implemented by digital circuitry. We study the performance of this system in the presence of typical linear channel characteristics. It is shown, via computer simulation and computation of the variances of errors, how the system corrects linear channel distortion.
59 citations
TL;DR: A technique for application of the popular fast Fourier transform (FFT) to the system identification problem and an iterative technique is discussed to avoid problems due to the circular nature of convolutions computed by the discrete Fouriertransform (DFT).
Abstract: A technique for application of the popular fast Fourier transform (FFT) to the system identification problem is outlined. Smoothing is obtained inherently in the transform and additionally by redundancy in the data. An iterative technique is discussed for the case of nonzero initial conditions and to avoid problems due to the circular nature of convolutions computed by the discrete Fourier transform (DFT).
4 citations