Showing papers on "Harmonic wavelet transform published in 1979"

Development of exponential Fourier transform and its application to electrical transients

Abstract: The paper describes the development of the numerical Fourier transform with exponential sampling. This is called the exponential Fourier transform (e.f.t.). The e.f.t. gives quite a high accuracy and a very long observation time with a small number of samples in comparison with a conventional numerical Fourier transform with equally spaced sampling. Thus, the computational efficiency of the e.f.t. is much higher than the conventional Fourier transform. Various calculated examples using the e.f.t. are given and are compared with the results obtained by the conventional Fourier transform. From the results the superiority of the e.f.t. compared with the conventional Fourier transform becomes clear. The e.f.t. would be very useful to deal with electrical transients with a very wide range of frequency or time.

Optimality of the Fast Fourier transform

Abstract: A graph-theoretic model for a class of linear algorithms computing the discrete Fourier transform of sequences of length a power of 2, the mformat~on flow network, is presented The information flow network correspondmg to the fast Fourier transform IS shown to be umquely optimal in tim class with respect to a naturally defined cost

Rate/Pitch modification of speech using the constant-Q transform

Abstract: Modification of the rate of occurrence of acoustic events without altering frequency content, and modification of pitch without changing time scale are presented as equivalent problems. While the short-time Fourier transform has been used to solve the rate modification problem, it is not a natural tool. It lacks the scaling property of the Fourier transform. The constant-Q transform, on the other hand, exhibits this property. A more natural rate/pitch modification system using the constant-Q transform is presented which performs well with rate/pitch changes by factors of between one-third and three.

Algorithm 545: An Optimized Mass Storage FFT [C6]

Abstract: The program is an implementation of the optimal sorting algorithm of the author [8] which allows a base-2 version of the Cooley-Tukey FFT algorithm [2-4] efficient access to a mass store array. Optimal sorting for the mass storage FFT has been determined independently by DeLotto and Dotti [5, 6], but in the author's version the emphasis is on \"in-place\" array modification. This results in slightly higher mass store I /O than the minimum, but requires no additional mass store working space. The method is a logical extension of the work of Singleton [9] and Brenner [1]. The program computes in place the discrete Fourier transform of a onedimensional or a multidimensional array. In the one-dimensional case the transform is defined by

D.F.T. computation by fast polynomial transform algorithms

Abstract: A new method is introduced for the fast computation of multidimensional discrete Fourier transforms (d.f.t.). We show that some multidimensional d.f.t.s are mapped efficiently into one-dimensional d.f.t.s by using a single polynomial transform and some auxiliary calculations. Since polynomial transforms can be computed without multiplications, this approach reduces significantly the number of operations over the conventional fast Fourier transform (f.f.t.) and is therefore attractive for image-processing applications.

The Problem of Calculating the Fast-Fourier Transform of a Step-Like Sampled Function

Abstract: The calculation of the fast fourier transform (FFT) for a step-like bounded function with unequal values at boundaries may be performed by using a convenient decomposition of the total curve into two elementary ones, one of them being a linear ramp. The method may be generalized to functions having asymptotic tails which may be approximated by simple analytic functions, the theoretical FFT of which is known.

Matrix multipliers for calculating orthogonal transforms

Abstract: The use of MOS transistors and weighted capacitors in a device to calculate the transform of a set of signal samples in 300ns will be discussed. Experimental results for a 16-point Hadamard and an 8-point complex Fourier transform will be given.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

Abstract: A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.

Parallel Optical Fourier Transform Techniques For Fourier Spectroscopy

Abstract: A survey of optical Fourier transform techniques is presented. The specific application considered is advanced focal plane Fourier spectroscopy in which multichannel Fourier analysis of long signals of modest band-width are required.

The Modification of Simple Images by Fourier Transform Manipulation

Abstract: Knowledge of how an image is changed by a given modification of its Fourier transform is important when attempting to find solutions to problems in image processing. Several types of filters were used to modify the Fourier transforms of an edge and a bartarget. The images were reconstructed from the modified transforms to determine the change produced by a given modification. Various regions of the Fourier transform determine specific characteristics of the image. The amplitude of the low frequencies controls the form and average level of the image, while the amplitude of the high frequencies effects sharp transitions and noise.

Parallelism in the computation of the FFT and the WFTA

Abstract: Arithmetic concurrencies, such as those found in special-purpose fast Fourier transform (FFT) hard-ware, are surveyed and categorized. Similar structures are then derived for the Winograd Fourier transform algorithm (WFTA). Relative time-efficiency plots are obtained for the 1024-point radix-4 FFT and the 1008-point WFTA as a function of the number of real arithmetic operations executable in parallel. This comparison shows that the relative time efficiency of the two algorithms in sequential computations generally carries over to cases where arithmetic parallelism is exploited.

Spatial filtering with a photographic replica of the Fourier transform of a half-tone picture

Abstract: Spatial filtering of the Fourier transform of a newspaper picture is achieved using a photographic negative of the Fourier transform generated by illumination of a small portion of the object. The results show improvement over those of simple pinhole spatial filtering. Also described is the use of photographically reduced array of dots as a spatial filter, giving slightly inferior results but greater flexibility of use. The optical system used incorporates a 2 mW He-Ne laser as the source.

Do not use a chirp to test a DFT program

Abstract: It is shown that the choice of a chirp waveform is a poor one for testing most algorithms which compute the discrete Fourier transform The Winograd-Fourier transform algorithm is especially susceptible to program bugs which will not be detected by computing the transform of a chirp sequence