Topic
Harmonic wavelet transform
About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.
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Book•
01 Dec 1993
TL;DR: In this paper, the authors introduce the idea of joint probability distributions and average for linear systems and their response to random vibrational signals. But they do not discuss the relationship between these distributions and the average.
Abstract: 1. Introduction To Probability Distributions And Averages. 2. Joint Probability Distributions, Ensemble Averages. 3. Correlation. 4. Fourier Analysis. 5. Spectral Density. 6. Excitation - Response Relations For Linear Systems. 7. Transmission Of Random Vibration. 8. Statistics Of Narrow Band Processes. 9. Accuracy Of Measurements. 10. Digital Spectral Analysis I: Discrete Fourier Transforms. 11. Digital Spectral Analysis II: Windows And Smoothing. 12. The Fast Fourier Transform. 14. Application Notes. 15. Multi-Dimensional Spectral Analysis. 16. Response Of Continuous Linear Systems To Stationary Random Excitation. 17. Discrete Wavelet Analysis.
855 citations
TL;DR: In this paper, the linear transform kernel for fractional Fourier transform is derived and the spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed.
Abstract: The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space–bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters are interleaved between several fractional transform stages, thereby increasing the number of degrees of freedom available in filter synthesis.
806 citations
TL;DR: In this review, the emerging role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the continuous and the discrete transform are considered in turn.
Abstract: The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex nonstationary signals. Its application to biosignal processing has been at the forefront of these developments where it has been found particularly useful in the study of these, often problematic, signals: none more so than the ECG. In this review, the emerging role of the wavelet transform in the interrogation of the ECG is discussed in detail, where both the continuous and the discrete transform are considered in turn.
794 citations
Proceedings Article•
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01 Aug 2004
TL;DR: A method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms, of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying.
Abstract: This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying. There is a connection between harmonic equations in rectangular and polar coordinate systems. The connection established here and used to create a very robust recursive algorithm for a conformal mapping calculation. There is also suggested a new ratio (and an efficient way of computing it) of two oscillative signal.
778 citations
TL;DR: An alternative projection algorithm is described that reconstructs a signal from azero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings.
Abstract: The completeness, stability, and application to pattern recognition of a multiscale representation based on zero-crossings is discussed. An alternative projection algorithm is described that reconstructs a signal from a zero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings. The reconstruction algorithm has a fast convergence and each iteration requires O(N log/sup 2/ (N)) computation for a signal of N samples. The zero-crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems. As an example, the implementation and results of a coarse-to-fine stereo-matching algorithm are described. >
743 citations