Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: The split radix was used to develop a fast Hartley transform algorithm, it is performed ''in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms'' as discussed by the authors.
Abstract: The split radix is used to develop a fast Hartley transform algorithm, it is performed `in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms.
40 citations
TL;DR: The Hilbert Huang transform (HHT) is introduced as an efficient means for analysis of bioacoustical signals and shows that HHT is a viable alternative to the wavelet transform.
Abstract: While marine mammals emit variant signals (in time and frequency), the Fourier spectrogram appears to be the most widely used spectral estimator. In certain cases, this approach is suboptimal, particularly for odontocete click analysis and when the signal-to-noise ratio varies during the continuous recordings. We introduce the Hilbert Huang transform (HHT) as an efficient means for analysis of bioacoustical signals. To evaluate this method, we compare results obtained from three time-frequency representations: the Fourier spectrogram, the wavelet transform, and the Hilbert Huang transform. The results show that HHT is a viable alternative to the wavelet transform. The chosen examples illustrate certain advantages. (1) This method requires the calculation of the Hilbert transform; the time-frequency resolution is not restricted by the uncertainty principle; the frequency resolution is finer than with the Fourier spectrogram. (2) The original signal decomposition into successive modes is complete. If we were to multiply some of these modes, this would contribute to attenuate the presence of noise in the original signal and to being able to select pertinent information. (3) Frequency evolution for each mode can be analyzed as one-dimensional (1D) signal. We not need a complex 2D post-treatment as is usually required for feature extraction.
39 citations
Patent•
18 Oct 2002TL;DR: In this article, a method for coding in frequency, module and phase a digital representation, in the space field, of a ring-shaped element, including the steps of: applying to any point of the element a polar conversion at constant angle, whereby the element is unfolded in rectangular form; transferring, to the frequency field, any points of the converted rectangular shape by means of a Fourier transform; filtering the discrete data resulting from the transfer by at least one real, bidimensional, band-pass filter, oriented along the phase axis; applying a Hilbert transform to the filtering results
Abstract: A method for coding in frequency, module and phase a digital representation, in the space field, of a ring-shaped element, including the steps of: applying to any point of the element a polar conversion at constant angle, whereby the element is unfolded in rectangular form; transferring, to the frequency field, any point of the converted rectangular shape by means of a Fourier transform; filtering the discrete data resulting from the transfer by means of at least one real, bidimensional, band-pass filter, oriented along the phase axis; applying a Hilbert transform to the filtering results; applying an inverse Fourier transform to the results of the Hilbert transform; and extracting phase and module information in the space field.
39 citations
TL;DR: In this paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases, including existence theorem, Parseval-type relationship and inversion formula.
38 citations
TL;DR: In this paper, a convolution of two functions ƒ and g, h = ǫ * g, defined by g, is introduced, where h is a function defined by
Abstract: (1) F(xu x2, • • • , xN) = fi(xi) + f2(x2) + +/N(XN) over the region R defined by xi+x2 + • • • +XN = X> x^O. Under various assumptions concerning the ƒ», this problem can be studied analytically; cf. Karush [ l ; 2] , and it can also be treated analytically by means of the theory of dynamic programming [3]. I t is natural in this connection to introduce a \"convolution\" of two functions ƒ and g, h = ƒ * g, defined by
38 citations