Showing papers on "Harmonic wavelet transform published in 1978"

On the use of windows for harmonic analysis with the discrete Fourier transform

Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

Reconstruction of an object from the modulus of its Fourier transform.

Abstract: We present a digital method for solving the phase-retrieval problem of optical-coherence theory: the reconstruction of a general object from the modulus of its Fourier transform. This technique should be useful for obtaining high-resolution imagery from interferometer data.

A new least-squares refinement technique based on the fast Fourier transform algorithm

Abstract: A new atomic-parameters least-squares refinement method is presented which makes use of the fast Fourier transform algorithm at all stages of the computation. For large structures, the amount of computation is almost proportional to the size of the structure making it very attractive for large biological structures such as proteins. In addition the method has a radius of convergence of approximately 0.75 A making it applicable at a very early stage of the structure-determination process. The method has been tested on hypothetical as well as real structures. The method has been used to refine the structure of insulin at 1.5 A resolution, barium beauvuricin complex at 1.2 A resolution, and myoglobin at 2 A resolution. Details of the method and brief summaries of its applications are presented in the paper.

Constant-Q signal analysis and synthesis

Abstract: A generalization of the short-time Fourier transform is presented which performs constant-percentage bandwidth analysis of time-domain signals. The transform is shown to exhibit frequency-dependent time and frequency resolution. A synthesis transform is also developed which provides an analysis-synthesis system which is an identity in the absence of spectral modification (given a mild analysis window constraint). The effect of stationary multiplicative modifications is discussed. Finally, similarities between the constant-Q spectral domain and the human auditory system are explored, and some implications for acoustic signal processing mentioned.

The Fourier-Mellin transform and mammalian hearing

Abstract: A combined Fourier–Mellin transform yields a representation of a signal that is independent of delay and scale change. Such a representation should be useful for speech analysis, where delay and scale differences degrade the performance of correlation operations or other similarity measures. At least two different versions of a combined Fourier–Mellin transform can be implemented. The simplest version (the ‖F‖2−‖M‖2 transform) completely eliminates spectral phase information, while a slightly more complicated version (the ?−? transform) preserves some phase information. Both versions can be synthesized with a Fourier transform and an exponential‐sampling algorithm. Exponential sampling produces a frequency scale distortion that is similar to the effect of the cochlea. The ‖F‖2−‖M‖2 transform can also be implemented with a bank of proportional bandwidth filters. If the relative phase between spectral components is preserved, then a Fourier–Mellin transformer can perform compression of linear‐period modulat...

An algorithm for the numerical evaluation of the Hankel transform

Abstract: A procedure is proposed for the numerical evaluation of the Hankel (Fourier-Bessel) transform of any integer order using the FFT algorithm The basis for the procedure is the "projection-slice" theorem associated with the two-dimensional Fourirer transform

Fourier transform spectroscopy

Abstract: Fourier transform spectroscopy is a technique that uses interference of light rather than dispersion to measure the spectrum of a substance. The basis of this technique is the Fourier-pair relationship between the interferogram (interference function) of a substance and its spectrum. This relationship and other important physical and mathematical principles of Fourier transform spectroscopy are reviewed, and the important role of mini-computers in the development and application of this technique is discussed.

An algorithm for generating fluctuations having any arbitrary power spectrum

Abstract: A calculational scheme is given for generating fluctuations which have any specified power spectrum. The fast computer-based algorithm makes use of a random number generator and fast Fourier transform (FFT) routine.

Gamma-ray imaging in Fourier space.

Abstract: A new coded-aperture configuration for gamma-ray imaging is described. It measures a single Fourier component of the object distribution at a time and does not require a position-sensitive detector. If, however, a position-sensitive detector is used, three-dimensional information about the source can be obtained.

An Optimal Algorithm for Computing Fourier Texture Descriptors

Abstract: The description of texture is an important problem in image analysis. Several methods in the literature require that local two-dimensional discrete Fourier transforms be computed as a first step in the texture description process. A chief limitation in these approaches has been the computational complexity of the transform calculation which has tended to limit the resolution of subsequent description and/or segmentation. It is shown here that through a suitable ordering of calculations, the transforms over a complete set of overlapping "texture windows" can be obtained efficiently. An algorithm is given and is shown to be time-optimal to within a constant factor.

Adaptive Fourier Transformation by Using Acousto-Optic Convolution

Abstract: An implementation of the chirp transform algorithm for performing a real-time Fourier transform is described. The implementation is based upon an acousto-optic (AO) convolver with a large time-bandwidth product. An instantaneous bandwidth of about 80 MHz was measured for the A0 Fourier transform with a dynamic range in excess of 60 dB for a cw time-gated waveform. Sidelobe errors of less than 0.8 dB were measured for uniformlyweighted pulses, with a corresponding phase error of less than 5". The adaptability of this acoustooptic implementation is demonstrated by the ease with which both the sidelobe weighting function and the time rate of the transform can be varied.

Fast-Fourier-transform processor using s.a.w. chirp filters

Abstract: A fast-Fourier-transform (f.f.t.) processor based on the chirp transform algorithm implemented with surface-acoustic-wave (s.a.w.) chirp filters is reported. Using commercially available s.a.w. devices the processor computes a 128-point (nominal) f.f.t. in 25 ?s, permitting real-time operation over 4 MHz bandwidth. Experimental results showing operation with sine and cosine inputs demonstrate processor performance in computing real and imaginary Fourier-transform components to an accuracy equivalent to 6 bits.

The fast Fourier transform by polynomial evaluation

Abstract: A description, leading to a program, for Fast Fourier Transform is given by means of the relationship to polynomial evaluation

The Fourier Transform: Properties and Applications

Abstract: Fourier analysis has been widely used in communication theory and electrical engineering for many, many years and is very well treated in text books covering these fields, but Fourier analysis is also very -useful in many other aspects and it is increasingly being used in all branches of the physical science.

Signal processing with number theoretic transforms and limited word lengths

Abstract: Number Theoretic Transforms (NTT's), unlike the Discrete Fourier Transform (DFT), are defined in finite rings and fields rather than in the field of complex numbers. Some NTT's have a transform structure like the Fast Fourier Transform (FFT) and can be used for fast digital signal processing. The computational effort and the signal-to-noise ratio (SNR) performance of linear filtering in finite rings and fields are investigated. In particular, the effect of limited word lengths, i.e., b \leq 16 , and long transform lengths on the SNR is analyzed. It is shown that for small word lengths and/or moderate to large transform lengths NTT filtering achieves a better SNR than FFT filtering with fixed-point arithmetic. Some new NTT's with a single- or mixed-radix fast transform structure are presented. While these NTT's may require special modulo arithmetic they achieve optimum transform length for any given word length b in the range 8 \leq b \leq 16 .

Alignment and Design Conditions for Optical Memory Systems Using Fourier Transform Holograms

Abstract: In this paper we present the displacement tolerances of optical system elements for recording and reconstructing Fourier transform holograms. The position, modification and magnification of the image are given as functions of the displacements and the parameters of the reference and reconstructing beam. Calculations are carried out on the basis of the scalar wave theory using the paraxial approximation.

Cross-correlation Estimates of Telluric and Magnetotelluric Parameters

Abstract: Procedures using cross-correlation functions to analyze telluric and magnetotelluric field data can be designed which, in certain applications, are more efficient than conventional techniques using fast Fourier transforms. One such application, involving the processing ofband-limited data, is presented here. The linear coupling relations between fields in a limited frequency band are estimated from transient time series by minimizing, in a least squares sense, the residuals between observed and predicted values of the frequency coefficients. The resulting normal equations contain integral averages over the continuous auto- and cross-energy spectra which are efficiently evaluated as Fourier transforms of windowed auto- and cross-correlation functions in the time domain.

Fast Fourier analysis and synthesis system - has Fourier transformer with Fourier processor having independent input and outputs

Abstract: In the fast Fourier processor, Fourier analysis of the first signals and Fourier synthesis of the second signals takes place in brief alternation. The same fast fourier processor is used for Fourier analysis and Fourier synthesis and has the same linking instruction and the same store with the same coefficient. A sorting device controlled by the word cycle of the input signals of the processor separates the components of the signals generated by Fourier analysis from the components of the signals generated by Fourier synthesis. The sorting device also arranges the sequences of the signal components.