Showing papers on "Harmonic wavelet transform published in 1970"
TL;DR: A novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars is described.
Abstract: This paper describes a novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars. The technique is based on the use of serial storage for data and intermediate results and multiple arithmetic units each of which carries out a sparse Fourier transform. Details of the system are described for data sample sizes that are binary multiples, but the technique is applicable to any composite number.
127 citations
IBM1
TL;DR: Alternative methods for the estimation of spectra are described and compared and general questions of statistical variability, the use of regression methods to smooth the periodogram, and use of time sectioning of the data to either smooth or to investigate non-stationarities in the data are discussed.
51 citations
34 citations
TL;DR: This paper presents the results of the fast Fourier transform in sufficient detail that interested nonexperts can obtain the computer algorithm, and the necessary label permutations, and points out the well known utility of base 2.
Abstract: The fast Fourier transform is usually described as a factorization. Recently this has been done in matrix terms. In this paper we present these results in sufficient detail that interested nonexperts can obtain the computer algorithm, and the necessary label permutations. We also count the number of arithmetic operations required in the calculation and point out the well known utility of base 2, both because of mathematical and machine hardware considerations. A simple FORTRAN program based on these ideas is included.
20 citations
TL;DR: It is concluded that the Blackman-Tukey technique is more effective than the FFT approach in computing power spectra of short historic time series, but for long records the fast Fourier transform is the only feasible approach.
Abstract: Since controversy has arisen as to whether the Blackman-Tukey or the fast Fourier transform (FFT) technique should be used to compute power spectra, single and cross spectra have been computed by each approach for artificial data and real data to provide an empirical means for determining which technique should be used. The spectra were computed for five time series, two sets of which were actual field data. The results show that in general the two approaches give similar estimates. For a spectrum with a large slope, the FFT approach allowed more window leakage than the Blackman-Tukey approach. On the other hand, the Blackman-Tukey approach demonstrated a better window closing capability. From these empirical results it is concluded that the Blackman-Tukey technique is more effective than the FFT approach in computing power spectra of short historic time series, but for long records the fast Fourier transform is the only feasible approach.
19 citations
TL;DR: In this article, an efficient method for inverting Laplace transforms using the fast Fourier transform is indicated, where sources of error are identified as well as the manner in which the parameters involved control them.
Abstract: An efficient method is indicated for inverting Laplace transforms using the fast Fourier transform. Sources of error are identified as well as the manner in which the parameters involved control them. It is shown how weighting of the Fourier coefficients can be used to improve numerical efficiency.
15 citations
TL;DR: The analysis of arbitrary time samples of signals of interest in terms of a Fourier series in effect forces the signal to be periodic with a fundamental period equal to the sample length.
Abstract: The analysis of arbitrary time samples of signals of interest in terms of a Fourier series in effect forces the signal to be periodic with a fundamental period equal to the sample length. This causes sinusoidal components in the signal that are not harmonic in the sample interval to appear to be discontinuous at the ends of the periods; each such component leads to a complete set of the harmonic terms determined by the analysis. The determination of the inharmonic sinusoidal components can be improved by taking suitable combinations of the coefficients determined by the analysis, or by a weighting of the input data to remove the discontinuity. It is shown that improvements of the convergence are accompanied by a corresponding broadening of the principal response.
13 citations
01 Jul 1970
TL;DR: In this paper, a fast Fourier transform technique is described for the approximate numerical evaluation of distribution functions directly from characteristic functions, which can be used to estimate the distribution function directly from the characteristic function.
Abstract: A fast Fourier transform technique is described for the approximate numerical evaluation of distribution functions directly from characteristic functions Examples are presented
12 citations
TL;DR: New and simple derivations for the two basic FFT algorithms are presented that provide an intuitive basis for the manipulations involved and reduce the operation to the calculation of a large number of simple two-data-point transforms.
Abstract: The fast Fourier transform (FFT) provides an effective tool for the calculation of Fourier transforms involving a large number of data points. The paper presents new and simple derivations for the two basic FFT algorithms that provide an intuitive basis for the manipulations involved. The derivation for the "decimation in time" algorithm begins with a crude analysis for the zero frequency and fundamental components using only two data samples, one at the beginning and the second at the midpoint of the period of interest. Successive interpolations of data points midway between those previously used result in a refinement of the amplitudes already determined and a first value for the next higher order coefficients. The derivation of the "decimation in frequency" algorithm begins by resolving the original data set into two new data sets, one whose transform includes only even harmonic terms and a second whose transform includes only odd harmonic terms. Since the first of the two new data sets repeats after the midpoint, it can be transformed using only the first half of the data points. The second of the new data sets is multiplied by the negative fundamental function, thereby reducing its order by one and converting it into a data set that transforms into even harmonics only; in this form it can also be transformed using only the first half of the data set. Successive applications of this procedure result finally in reducing the operation to the calculation of a large number of simple two-data-point transforms.
12 citations
TL;DR: In this article, a complex BIFORE transform is defined and elementary properties of the transform are developed, and the complexity of the transformation is analyzed and the properties of its properties are analyzed.
Abstract: A complex BIFORE transform is defined and elementary properties of the transform are developed.
TL;DR: In this paper, Coooley and Tukey's fast Fourier transform algorithm for two dimensional complex data has been modified so as to reduce the storage space and computation time to half.
Abstract: Cooley andTukey's fast Fourier transform algorithm for two dimensional complex data has been modified so as to reduce the storage space and computation time to half. The modified version has enabled us to Fourier transform aeromagnetic field over twice the area that could be covered by the original method. From the Fourier transform we computed radial spectrum, which could be approximated by three straight line segments whose slopes are related to the depths of the various magnetic layers. The computed depths are: 1090', 2600', and 7200'.
TL;DR: In this article, a new technique of holographic multiplexing based on Fourier transform holography and the division of the aperture field has been briefly discussed, and preliminary experimental results have been presented.
TL;DR: In this article, it is shown that the Laguerre transform is more convenient than the Poisson transform for signal analysis; indeed, given a signal, one can immediately write the Lenguerre expansion of this signal, while, for the poisson transform, additional and tedious binomial-weighted summations are required.
Abstract: Simulation of analogue signals by Laguerre-transformation sampling is considered in the letter. It is shown that the Laguerre transform is more convenient than the Poisson transform for signal analysis; indeed, given the Laguerre transform of a signal, one can immediately write the Laguerre expansion of this signal, while, for the Poisson transform, additional and tedious binomial-weighted summations are required. Also, it is shown that the Laguerre transform corresponds to a simple signal measurement.
01 Nov 1970
TL;DR: A method is proposed for computing the discrete Fourier transform of complex data whose real and imaginary parts are represented as voltages and operational amplifiers and resistors are the only computing elements required.
Abstract: A method is proposed for computing the discrete Fourier transform of complex data whose real and imaginary parts are represented as voltages. Operational amplifiers and resistors are the only computing elements required.
TL;DR: In this article, a subband Hilbert transform based on subband decomposition is proposed for analytic signal processing in single-sideband amplitude modulation and demodulating frequency-modulated signals.
Abstract: A new and fast approximate Hilbert transform based on subband decomposition is presented. This new algorithm is called the subband (SB)-Hilbert transform. The reduction in complexity is obtained for narrow-band signal applications by considering only the band of most energy. Different properties of the SB-Hilbert transform are discussed with simulation examples. The new algorithm is compared with the full band Hilbert transform in terms of complexity and accuracy. The aliasing errors taking place in the algorithm are found by applying the Hilbert transform to the inverse FFT (time signal) of the aliasing errors of the SB-FFT of the input signal. Different examples are given to find the analytic signal using SB-Hilbert transform with a varying number of subbands. Applications of the new algorithm are given in single-sideband amplitude modulation and in demodulating frequency-modulated signals in communication systems. Key Words : Fast Algorithms, Hilbert Transform, Analytic Signal Processing.
TL;DR: In this article, a transform with a square-wave kernel is proposed to complement the fast Fourier transform (f.f.t.) algorithm, being a trapezoidal integration rule, giving errors in the tails of spectra.
Abstract: Unless inconveniently high sampling rates are used, the fast-Fourier-transform (f.f.t.) algorithm, being a trapezoidal integration rule, gives errors in the tails of spectra. A transform with a square-wave kernel, which can be evaluated accurately in a simple manner, is proposed to complement the f.f.t. An example involving measured data is included.
01 Jan 1970
TL;DR: Algorithm for inverse Laplace transformation of irrational transfer function via fast Fourier transform is presented in this article, where the transformation is based on the fast-fourier transform (FFT).
Abstract: Algorithm for inverse Laplace transformation of irrational transfer function via fast Fourier transform
TL;DR: In this paper, a method for the formation of the Fourier transform hologram of a 3D object scene such that the reconstructed image is also 3D in nature showing parallax effect is discussed.
Abstract: A method has been discussed which enables the formation of the Fourier transform hologram of a three‐dimensional object scene such that the reconstructed image is also three‐dimensional in nature showing, say, parallax effect. Supporting experimental result has been presented.
Proceedings Article•
01 Jan 1970
TL;DR: Algorithm for Fast Two Dimensional Fourier Transform requiring logarithm additions and multiplication as discussed by the authors. But this algorithm is not suitable for fast two dimensional Fourier transform and requires a large number of inputs.
Abstract: Algorithm for Fast Two Dimensional Fourier Transform requiring logarithm additions and multiplication
01 Jan 1970
TL;DR: In this paper, the fast Fourier transform (FFT) algorithm was used as a highly efficient numerical means for the analysis of transient scattering phenomena, which can best be exploited when additional characteristics of the radar system such as the actual transmitted waveform and the receiver transfer function are taken into account.
Abstract: The fast Fourier transform algorithm can be used as a highly efficient numerical means for the analysis of transient scattering phenomena. Examples illustrating the performance of this method are given for an incident pulse of Gaussian shape. It is noted that such a technique can best be exploited when additional characteristics of the radar system such as the actual transmitted waveform and the receiver transfer function are taken into account.
TL;DR: In this paper, a comparison between a system identification method using the fast Fourier transform and one which is optimal is made, and it is shown that for systems with long settling times the transform method possesses computational advantages but at the cost of accuracy.
Abstract: Comparison between a system identification method using the fast Fourier transform and one which is optimal is made. The comparison shows that for systems with long settling times the transform method possesses computational advantages but at the cost of accuracy.
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TL;DR: The letter shows the limiting factors in a pipeline FFT and allows its performance to be effectively compared with a random access oriented FFT.
Abstract: This letter contains a graph paper summarizing many properties of Fourier transforms and fast Fourier transform (FFT) devices. It shows the interrelationships among data block length, frequency resolution sampling rate, FFT stages, and other related variables. The letter shows the limiting factors in a pipeline FFT and allows its performance to be effectively compared with a random access oriented FFT.