Showing papers on "Harmonic wavelet transform published in 1988"

The fast Fourier transform and its applications

Abstract: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

The evolution of the wave function in a curve crossing problem computed by a fast Fourier transform method

Abstract: We develop a unitary fast Fourier transform method for solving time dependent curve crossing problems. The procedure is described in detail and is illustrated by calculations for a two curve, one‐dimensional example. The time evolution of the wave function and mean nuclear positions and energies for each curve are shown and discussed.

The Wavelet Transform for Analysis, Synthesis, and Processing of Speech and Music Sounds

Abstract: The wavelet transform is a recent method of signal analysis and synthesis (Grossmann and Morlet 1984; Grossmann et al. 1987). It analyzes signals in terms of wavelets-functions limited both in the time and the frequency domain. In comparison, the classical Fourier analysis method analyzes signals in terms of sine and cosine wave components that are not limited in time. The wavelet transform is related to granular analysis/synthesis, first suggested by Gabor (1946). Granular synthesis has been implemented by Roads (1978) and Truax (1988). Rodet (1985) and Li6nard (1984) use adapted grains for speech signals; however, these implementations do not attempt to reconstruct an arbitrary given signal. The Gabor method uses an expansion of a function into a two-parameter family of elementary wavelets that are obtained from one basic wavelet

The circular harmonic transform for SPECT reconstruction and boundary conditions on the Fourier transform of the sinogram

Abstract: The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary. An important special case also considered is the linear (unattenuated) Radon transform (LRT). The solution is on the form of an orthogonal function expansion matched to projections that are in parallel-ray geometry. This property allows for efficient and accurate processing of the projections with fast Fourier transform (FFT) without interpolation or beam matching. The algorithm is optimized by the use of boundary conditions on the 2-D Fourier transform of the sinogram. These boundary conditions imply that the signal energy of the sinogram is concentrated in well-defined sectors in transform space. The angle defining the sectors depends in a direct way on the radius of the field view. These results are also obtained for fan-beam geometry and the linear Radon transform (the Fourier-Chebyshev transform of the sinogram) to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates. >

Wavelet Transforms and Edge Detection

Abstract: A wavelet transform of a function is, roughly speaking, a description of this function across a range of scales. We use the technique of wavelet transforms to detect discontinuities in the n-th derivative of a function of one variable.

The arithmetic Fourier transform

Abstract: Preliminary results are presented on the VLSI design and implementation of a novel algorithm for accurate high-speed Fourier analysis and synthesis. The arithmetic Fourier transform (AFT) is based on the number-theoretic method of Mobius inversion. Its computations proceed in parallel, and the individual operations are very simple. Except for a small number of scalings in one state of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if ideal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D (analog-to-digital) conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Further simplifications are obtained by using delta modulation to represent the input function in digital form, so that only binary (or preferably, ternary) sequences needs to be processed in the parallel computations. The required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation. >

A new polar Fourier transform for computer-aided tomography and spotlight synthetic aperture radar

Abstract: An algorithm for calculating the Fourier transform of certain discrete measures supported on a two-dimensional polar grid is described. The algorithm utilizes a modified Bluestein chirp algorithm to directly calculate the Fourier transform values over a rectangular grid. Applications to computer-aided tomography and spotlight synthetic aperture radar are described. >

Picture signal processor, picture signal coder and picture signal interpolator

Abstract: An image signal processor in which the conversion process of a picture signal is performed in block unit, not in frame unit, and in order to raise the speed of the process, besides an orthogonal transform matrix, the products between the orthogonal transform matrix and matrices for realizing picture resolution conversion, image manipulation processes such as expansion, compression and rotation, and various kinds of linear filtering are provided in a coefficient memory as new transform matrices, and these transform matrices are properly changed-over in accordance with the content of the pertinent transform, thereby to perform an orthogonal transform or an inverse orthogonal transform.

A systolic circuit for fast Hartley transform

Abstract: The authors present a systolic circuit for computing a fast algorithm performing the discrete Hartley transform (DHT). The proposed architecture employs a systolic elevator concept and CORDIC processors. The elevator assures local communications in the proposed algorithm, and the CORDIC processor makes it possible to enhance processing speed and exploit parallelism. The architecture appears to be regular and, therefore, very attractive for VLSI realizations. The computational cost necessary for computing the DFT (discrete Fourier transform) is also discussed with respect to other architectures. >

Reed-Muller transform image coding

Abstract: A new technique using the Reed-Muller transform has been applied for image data bandwidth compression. The basic concept wad derived from the Reed-Muller canonical expansion of boolean functiona. The transform over Galois field 2 was investigated in this work. A fast algorithms has been developed for the computation of the Reed-Muller transform. Simulation results indicate that the Reed-Muller transform provides good quality reconstructed images with approximately 2.5 bits per pixel for monochrome images. The computational efficiency and simple hardware realization of this transform might make it a viable candidate for certain real time image data compression applications.

VLSI implementation of a 16*16 DCT

Abstract: The implementation of a 16*16 discrete cosine transform (DCT) chip using a concurrent architecture is presented. The chip is designed for real-time processing of 14.3 MHz sampled video data. The architecture and accuracy studies for finite-wordlength processing are discussed. The chip was implemented, tested, and found to be fully functional. Possible variations are presented for multipurpose (variable transform sizes, forward-backward transform) applications. >

Time-frequency and time-scale (signal processing)

Abstract: General results are presented for time-frequency and time-scale methods. Attention is given to both linear (short-time Fourier transform, wavelet transform) and bilinear (Wigner-Ville distribution, affine Wigner distribution) approaches, with emphasis put on their relationships. Also considered is the relationship of the methods examined to such approaches as constant-Q analysis and ambiguity functions. >

Automated two speaker separation system

Abstract: An algorithm designed to improve results for separating two voices simultaneously recorded on a single channel is presented. A variable frame size orthogonal transform and a spectral matching technique are used. A multistep pitch detection scheme is proposed which includes a traditional autocorrelation function, a modified autocorrelation, the average magnitude difference function, and a look-forward and look-backward double checking scheme. The orthogonal transforms utilized include the fast Fourier transform and the fast triangular transform. For a variable frame size transform, a prime factor fast Fourier transform has been developed. The execution of the process is automated and implemented on the IBM-PC, VAX 8650, and HP 9000. Intelligibility tests using simple quantitative measures have been performed on the separated signals. An extension of the problem to the three-speaker case is reported. >

An improved bit-reversal algorithm for the fast Fourier transform

Abstract: The recording effect of the fast Fourier transform is considered which requires that the elements of the data array be permuted by bit-reversing the array index. The bit-reversal algorithm given by B. Gold and C.M. Rader (1969) is referred to. Several improvements are made to this algorithm that result in improved efficiency. A closed-form expression is derived for the largest index that must be bit-reversed. A computational analysis is given, comparing the original and modified algorithms. >

A functional program for the fast Fourier transform

Abstract: This paper is written as a contribution to the Parallel Reduction Machine Project. Its purpose is to present a functional program for a well-known application of the fundamental algorithmic method Fast Fourier Transform for multiplication of polynomials. This in order to verify experimentally two claims by functional programmers [BvL]: (i) functional programming is good for writing structured software; better so than the so-called imperative von Neumann-languages. (ii) functional programming allows for a parallel evaluation of subexpressions, provided a proper implementation.

The performance of Fourier transform division multiplexing schemes on peak limited channels

Abstract: Inherent in the method of Fourier transform division multiplexing (FTDM) is the possibility that the FTDM encoder will yield spurious power bursts, which can affect the linearity of the channel. A common way for dealing with such bursts is to clip the signal at some predetermined peak power level. The authors obtain explicit formulas for the probability distributions of such bursts and for the errors that the clipping induce in the decoder. The formulas can help the FTDM code designer to decide on an appropriate average power constraint. >

A novel radix-2 pipeline architecture for the computation of the DFT

Abstract: A radix-two discrete Fourier transform (DFT) algorithm is derived which supports a pipeline architecture realization. The amount of necessary multipliers for the pipeline structure can be reduced by a factor up to four compared to the conventional and most often used radix-2 pipeline-FFT. This reduction is obtained without sacrificing computational speed. Several applications of digital signal processing require dedicated hardware to compute the DFT and/or its inverse in order to cope with the fast processing speeds which are needed. >

Joint fourier transform processor

Abstract: A joint Fourier transform processor can be used as a conventional coherent optical processor In principle, the joint transform processor can perform all the optical data processing that a conventional coherent optical processor can offer Sample illustrations for signal extraction and image subtraction are given The major advantages of the joint transform processor must be (1) the avoidance of synthesizing a matched spatial filter, (2) higher space-bandwidth product, (3) lower spatial carrier frequency requirement, (4) higher output diffraction efficiency, etc

Broadband beamforming on the 2-D transform plane

Abstract: On taking the 2D Fourier transform of the output of a linear array, a ridge will appear on the frequency-wave number plane if a source is present. The slope of this ridge is determined by the direction of arrival of the wavefront. Two methods are proposed to estimate this slope. The first one takes the sums of the squared magnitude of the transform along predetermined slopes to find the maximum sum. The second one requires less computation; it first locates all the maxima of the transform. A weighted-least-squares fit is then taken through these maxima to give a slope estimation. The multisource case is considered, and properties and statistics of the beamformer, together with simulation results, are given. >

A fast algorithm of running fourier transform

Abstract: A short-time Fourier transform can be derived by low-pass filtering of the product of an input signal and exp(j2°ft). According to this method, called the Running Fourier Transform (RFT) in this paper, running power spectra with arbitrary center frequencies and arbitrary Q values can be obtained. This paper proposes a fast algorithm of discrete RFT (FRFT). In the FRFT, a first-order lag system is adopted as the low-pass filter (LPF), and by approximating the impulse response of the LPF with a step function, the amount of multiplications is reduced. The calculation of the complex exponentials is omitted by referring to a table of sin(2°k/K) (k =0, …, K).

The Fast Hartley Transform as an Alternative to the Fast Fourier Transform

Abstract: : A comparison is made between the Discrete Hartley Transform and Discrete Fourier Transform algorithms. the Fast Hartley Transform is examined as an alternative to the Fast Fourier Transform for signal processing in the Jindalee Over The Horizon Radar project. Keywords: Algorithms; Fast Fourier transforms; Signal processing; Over the horizon radar; Australia.

Fast Fourier Transforms: A Review

Abstract: The purpose of this paper is to provide a detailed review of the Fast Fourier Transform. Some familiarity with the basic concepts of the Fourier Transform is assumed. The review begins with a definition of the discrete Fourier Transform (DFT) in section 1. Directly evaluat­ ing the DFT is demonstrated there to be an 0 (N 2 ) process.

On the block least squares adaptive digital filters realized using the fast Fourier transform

Abstract: The authors formulate a block-based least-squares problem in the frequency domain. They then develop computationally efficient block least-squares algorithms that can be realized using the fast Fourier transform. They also present computer simulation results demonstrating the convergence characteristics of the proposed algorithms. >

On a Fast Piece-Wise Linear Hough Transform PLHT and its Application.

Abstract: Replacing the Hough calculation of the trigonomeric functions, sine and cos0,by the piece-wise linear Hough function(PLH), the basic cost for the sine , cose and the multiplications is removed. The PLH function is directly introduced from the usual Hough function. The PLH function inherits the basic properties of the usual Hough function from the view point to extract the line patterns from the pattern space. The computing cost of the PLH transform was reduced to about 1/6 of that of the usual Hough transform. It was also investigated that an additional property of the PLH transform contributes to reduce the memory cost to about 70 % of the usual Hough transform. Hough transform is one of the important methods to extract line patterns from the noisy and unclustered points of the image. As the edge or line patterns are the essential features in several industrial vision systems, it is practically required to make the Hough transform efficient from the view point of the computing and memory costs. A new fast Hough transform algorithm is introduced and its application is shortly presented in this paper. From this point of view, it is important to reduce the computing cost to utilize the Hough transform in several application. One of the factors in order to realize this cost reduction is to reduce the number of Hough calculations with respect to the number of edge points and and resolution numbers of the parameter space. It is still expectative to decrease the computing cost for the core Hough calculation defined by eq.(l). x.cos 0 + y.sin 8 (1) * =€I : perpendicular angle from x-axis JJ : the length of the perpendicular line In this paper, replacing Hough calculation of the trigonometric functions by the piecewise linear Hough(PLH) function which is composed of m pieces of line segments, the basic cost for the sine , cose and multiplications can be removed. It is shown in section 3 that the PLH function inherits the basic properties of the usual Hough function from the view point of to extract line patterns from the pattern space, and a few modifications of the pattern behavior in pattern space are also presented. In section 4, an new algorithm of piece-wise linear Hough transform(PLHT) is introduced, and some experimental results of PLHT are presented to demonstrate the reduction of the computing cost using an image of industrial engine parts. 2. Piece-wise Linear Hough Function 2.

A 4.8 kbps voice coding using pitch synchronous DFT

Abstract: The authors propose a 4.8-kbps voice-coding algorithm using pitch-synchronous discrete Fourier transform (DFT). This algorithm combines time-scale compression with pitch-synchronous DFT spectrum coding. It also discards the time-compressed signal-phase information and the nonharmonic spectral components to reduce the amount of information processes. Simulation results show that the reproduced sound quality is good. Processing delay is about 80 ms, without including operation time. >

Transform domain edge enhancement of digital radiographs

Abstract: An enhanced digital radiograph is obtained by multiplication between the digital radiograph and the digital Fourier transform of the second derivative of the Gaussian function ( Delta /sup 2/g) and inverse transformation, and the subsequent histogram equalization. Because image data includes only real values, the purely real-numbered transform, called the fast Hartley transform (FHT) is used to perform a digital Fourier transform of the image data. Preliminary results suggest that the transform of the Laplacian of the Gaussian may provide a more effective edge enhancement for medical imagery than space-domain convolution techniques such as the Sobel operator. >