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Showing papers on "Harmonic wavelet transform published in 1982"


Proceedings ArticleDOI
01 May 1982
TL;DR: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude, for applications such as speech processing.
Abstract: This paper presents various conditions that are sufficient for reconstructing a discrete-time signal from samples of its short-time Fourier transform magnitude. For applications such as speech processing, these conditions place very mild restrictions on the signal as well as the analysis window of the transform. Examples of such reconstruction for speech signals are included in the paper.

79 citations


Journal ArticleDOI
TL;DR: In this article, a steplike waveform is converted into a duration-limited one which preserves the spectrum of the original waveform and is suitable for discrete Fourier transform (DFT) computations.
Abstract: A steplike waveform which has attained its final value is converted into a duration-limited one which preserves the spectrum of the original waveform and is suitable for discrete Fourier transform (DFT) computations. The method, which is based upon the response of a time-invariant linear system excited by a rectangular pulse of suitable duration, is first applied to continuous waveforms and then to discrete (sampled) waveforms. The difference (errors) between the spectra of a continuous waveform and a discrete representation of it are reviewed.

74 citations



Journal ArticleDOI
TL;DR: A modified version of Burrus' prime factor fast Fourier transform program is described, which implements the in-place, in-order algorithm for variable transform sizes.
Abstract: This paper describes a modified version of Burrus' prime factor fast Fourier transform program. The modifications produce a general-purpose program which implements the in-place, in-order algorithm for variable transform sizes. Speed tests show the resulting program to be faster than a program using a separate reordering pass.

34 citations



Journal ArticleDOI
TL;DR: Two new algorithms that are more convenient for computation than existing ones for the slant transform are developed and reveal the close relationship between theSlant transform and the Walsh-Hadamard transform.
Abstract: Two new algorithms that are more convenient for computation than existing ones for the slant transform are developed. These algorithms reveal the close relationship between the slant transform and the Walsh-Hadamard transform and demonstrate that the slant transform may be approached by a series of steps which gradually change the transform from a Hadamard or Walsh transform to a slant transform.

23 citations


Journal ArticleDOI
TL;DR: A new algorithm for the calculation of the Fourier transform of sampled time functions is described, based on second‐degree polynomial interpolations between the sample points, which was found to be significantly more accurate than the conventionally used discrete Fouriertransform (DFT).
Abstract: A new algorithm for the calculation of the Fourier transform of sampled time functions is described. The algorithm is especially applicable to the Fourier analysis of nonperiodic signals which are not band limited. The method is based on second‐degree polynomial interpolations between the sample points. The obtained continuous approximation of the signal allows the determination of the Fourier transform analytically. In the case of exponentially decaying functions the algorithm was found to be significantly more accurate than the conventionally used discrete Fourier transform (DFT). The computing time is only about twice the time required by the fast Fourier transform (FFT) algorithm.

16 citations


Journal ArticleDOI
TL;DR: In this article, the Modified-KWE (MKWE) method provides two quadrant data set in 2-D Fourier space which is essential for the accurate image representation of the NMR spin density.
Abstract: Direct Fourier transform NMR tomographic method originally proposed by Kumar-Welti-Ernst(KWE) has been modified by double spin echo technique to improve the image quality. This new Modified-KWE(MKWE) method provides two quadrant data set in 2-D Fourier space which is essential for the accurate image representation of the NMR spin density. Further improvement of the MKWE method using the slice encoding technique and spin echo measurement time is also investigated.

14 citations


Journal ArticleDOI
TL;DR: In this paper, the first experience with a three-level double resonance experiment performed with a microwave Fourier transform spectrometer was described by a theoretical treatment based on three level Bloch equations.
Abstract: We present the first experience with a three-level double resonance experiment performed with a microwave Fourier transform spectrometer. The results are described by a theoretical treatment based on three-level Bloch equations.

11 citations



Journal ArticleDOI
TL;DR: A simple derivation of Glassman's general N fast Fourier transform, and corresponding FORTRAN program, is presented, based upon a representation of the discrete Fourier Transform matrix as a product of sparse matrices.
Abstract: : A simple derivation of Glassman's general N fast Fourier transform, and corresponding FORTRAN program, is presented. This fast Fourier transform is based upon a representation of the discrete Fourier transform matrix as a product of sparse matrices. (Author)

Journal ArticleDOI
TL;DR: A third possibility is suggested: a direct Fourier transform which takes advantage of certain properties of a spike train and works much faster than a common Fouriertransform.
Abstract: A spike train may be represented by a superposition of Dirac delta-functions. One of the simplest ways of converting such a comb function into a continuous function is to use a Fourier transform. In general there are two possibilities, both of which have their disadvantages: the direct transform which is extremely time-consuming, and the fast Fourier transform of the low pass filtered comb function; the latter method, although quicker, often requires a greater storage capacity than is readily available. In the present paper, therefore, a third possibility is suggested. Essentially, it is a direct Fourier transform which takes advantage of certain properties of a spike train. The corresponding algorithm works much faster than a common Fourier transform.

Journal ArticleDOI
TL;DR: In this article, a s-spline fit is made to the input function, and the Fourier transform of the set of B-splines is performed analytically for a possibly nonuniform mesh.
Abstract: Finite Fourier integrals of functions possessing jumps in value, in the first or in the second derivative, are shown to be evaluated more efficiently, and more accurately, using a continuous Fourier transform (CFT) method than the discrete transform method used by the fast Fourier transform (FFT) algorithm. A s-spline fit is made to the input function, and the Fourier transform of the set of B-splines is performed analytically for a possibly nonuniform mesh. Several applications of the CFT method are made to compare its performance with the FFT method. The use of a 256-point FFT yields errors of order 10~2, whereas the same information used by the CFT algorithm yields errors of order 10~7—the machine accuracy available in single precision. Comparable accuracy is obtainable from the FFT over the limited original domain if more than 20,000 points are used.

Journal ArticleDOI
TL;DR: In this article, a Fourier transform in the Glauber formalism of elastic scattering for hadron-helium was introduced, and a new way to choose this transform was introduced.
Abstract: We introduce a Fourier transform in the Glauber formalism of elastic scattering for hadron-helium. We discuss different classical choices of this Fourier transform and we introduce a new way to choose this transform. We compare differential cross-sections computed with different Fourier transforme with available experimental results.

Proceedings ArticleDOI
01 May 1982
TL;DR: A sampling method is developed to significantly reduce the error in the reconstructed sequence, and the error is found to increase as the number of non-zero points in the sequence increases and as the noise level increases.
Abstract: The effects of noise in the given phase on signal reconstruction from the Fourier transform phase are studied. Specifically, the effects of different methods of sampling the degraded phase, of the number of non-zero points in the sequence, and of the noise level on the sequence reconstruction are examined. A sampling method is developed to significantly reduce the error in the reconstructed sequence, and the error is found to increase as the number of non-zero points in the sequence increases and as the noise level increases. In addition, an averaging technique is developed which reduces the effects of noise when the continuous phase function is known. Finally, as an illustration of how the results in this paper may be applied in practice, Fourier transform signal coding is considered. Coding only the Fourier transform phase and reconstructing the signal from the coded phase is found to be considerably less efficient (i.e. a higher bit rate is required for the same mean square error) than reconstructing from both the coded phase and magnitude.

Journal ArticleDOI
TL;DR: This paper reports on the application of a new FFT algorithm, first described by Winograd, to the calculation of diffraction OTF that yields the same accuracy as that obtained by the Cooley-Tukey method but is up to four times faster.
Abstract: Although fast Fourier transform (FFT) algorithms based on the Cooley-Tukey method have been widely used for the computation of optical transfer function (OTF), the need for yet faster algorithms remains. This is particularly so since desk-top computers with modest speed and memory size have become essential tools in optical design. In this paper we report on the application of a new FFT algorithm, first described by Winograd, to the calculation of diffraction OTF. The algorithm is compared both in speed and in accuracy with the commonly used radix-2 FFT and with an autocorrelation method employing the Gaussian quadrature integration technique. It is found that the new algorithm yields the same accuracy as that obtained by the Cooley-Tukey method but is up to four times faster. Some other advantages and drawbacks are discussed.

Journal ArticleDOI
Clive Temperton1
TL;DR: Describing the development of fast Fourier transform routines for the vector-processing Cray-1 and Cyber 205 machines shows that multiple transforms can be implemented faster on the Cyber 205 (using 64-bit arithmetic on the 2-pipe model) than on the CRAY-1, provided that enough transforms are performed in parallel.

Journal ArticleDOI
TL;DR: The sectionalized Fourier Transform has many applications in time-domain signal processing using modern array digital computers and has proved advantageous in underwater acoustic applications.
Abstract: The sectionalized Fourier transform of a band-limited signal (defined as a Fourier transform which is computed over incremented temporal sections of the function) is equivalent to basebanding, filtering, and sampling the signal in time domain. Spectral windowing is employed, through appropriately summing a sequence of the Fourier transform bins, to control the passband and leakage characteristics of the resulting filter. This in turn controls the distortion of the signal induced as a result of the transform process. The use of the sectionalized Fourier transform is exploited to conveniently and rapidly map the cross-correlation envelope of narrow-band signals over the time-register Doppler-ratio (ambiguity) plane. By using the ambiguity kernel \exp(i2\pi\alphaft) as an approximation of signal time compression (or expansion), the coherence between transformed signals (along the Doppler-ratio axis) may further be expedited through use of the discrete Fourier transform. The resulting error is negligible when the time-bandwidth product of the process is less than the inverse of the maximum Doppler ratio employed. The resulting algorithms have proved advantageous in underwater acoustic applications. It is concluded that the sectionalized Fourier Transform has many applications in time-domain signal processing using modern array digital computers.

Proceedings ArticleDOI
01 May 1982
TL;DR: This paper compares and rank the KL, Fourier, Walsh-Hadamard, Haar, Discrete Cosine, Slant Walsh Hadamard and Slant Haar Transforms by their performance in applications and by the number of elementary operations they require.
Abstract: For several signal processing applications, the usefulness of Fast Unitary Transforms (FUT) is now well recognized [1-7]. For signal representation, filtering and encoding, it is well known that the Karhunen-Loeve (KL) Transform, based on signal statistics, is optimum in various senses, but the KL Transform is slow. Suboptimum FUT's allow a trade-off between performance and speed. In this paper, we compare and rank the KL, Fourier, Walsh-Hadamard, Haar, Discrete Cosine, Slant Walsh Hadamard and Slant Haar Transforms by their performance in applications and by the number of elementary operations they require. In encoding and filtering, recursive techniques are widely used and are generally fast. By considering both performance and computations we are able to compare directly recursive and transform algorithms. The comparison brings to light a performance versus computation bound for the two classes of processing techniques.

Journal ArticleDOI
TL;DR: An all-mirror system for coherent image processing is described in this article, where a parabolic mirror is used for unit magnification, panchromatic correction and the introduction of minimal scattering noise into the Fourier transform plane and the final image.
Abstract: An all-mirror system for application in coherent image processing is described. A system with a parabolic mirror offers advantages such as unit magnification, panchromatic correction and the introduction of minimal scattering noise into the Fourier transform plane and the final image. The Fourier transform properties of this system are acceptable for many applications.

Journal ArticleDOI
TL;DR: Novel concepts for simplification of the optical design of a time-integrating acousto-optical signal processor for real-time Fourier transformation are described, suitable for designing ultracompact devices.
Abstract: Novel concepts for simplification of the optical design of a time-integrating acousto-optical signal processor for real-time Fourier transformation are described. Fourier transforms of both pulsed and continuous signals, obtained from the triangular common-path interferometric setup, are demonstrated. Because of their simplicity, these concepts are suitable for designing ultracompact devices.

Proceedings ArticleDOI
03 May 1982
TL;DR: An integrated address sequencer for the Fast Fourier Transform is described and how this may be included in a high-speed signal processing peripheral is shown.
Abstract: This paper describes an integrated address sequencer for the Fast Fourier Transform. It also shows how this may be included in a high-speed signal processing peripheral.

Journal ArticleDOI
TL;DR: In this paper, a Michelson interferometer is used to record an interferogram, which is then Fourier transformed to obtain the spectrogram of the light source, and then the Fourier transform is applied to obtain a light source spectrogram.
Abstract: In the past years, the Journal has published a number of articles1–5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley–Tukey’s fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)

Journal ArticleDOI
TL;DR: An optimisation of the fast Fourier transform for two-dimensional transforms is described, followed by a discussion of a number of numeric-intensive techniques in image processing using this method.

Journal ArticleDOI
TL;DR: In this correspondence, a fixed-point error analysis is given for polynomial transforms computed using two's complement arithmetic and the results are extended for computing the mean-square error of a two-dimensional discrete Fourier transform (DFT) computed byPolynomial transform technique.
Abstract: In this correspondence, a fixed-point error analysis is given for polynomial transforms computed using two's complement arithmetic. The results are extended for computing the mean-square error of a two-dimensional discrete Fourier transform (DFT) computed by polynomial transform technique. Also, an earlier result derived by Nussbaumer [1] for comparing the rms error/rms result of the polynomial transform and the fast Fourier transform (FFT) has been modified.

Journal ArticleDOI
TL;DR: The software described here consists in a set of routines to compute the Fast Fourier Transform in a wide variety of situations, such as real-time signal analysis, image processing and analysis of disk resident, long strings of data.


Book ChapterDOI
G. Sampson1
01 Jan 1982