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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: In this paper, the relationship between the instantaneous frequencies of a signal in polar form and the phase of the corresponding Stockwell transform is analyzed using the stockwell transform and the corresponding results using a reciprocal Morlet wavelet transform are given for comparisons.
Abstract: The phase of a signal is analyzed using the Stockwell transform. In particular, the relationships between the instantaneous frequencies of a signal in polar form and the phase of the corresponding Stockwell transform are given. The corresponding results using a reciprocal Morlet wavelet transform are given for comparisons.
15 citations
TL;DR: Results and analysis substantiate the fact that proposed scheme is robust, highly sensitive, and shows considerably better performance than other similar-state-of-art schemes.
15 citations
10 Dec 1997
TL;DR: In this paper, a frequency weighted least squares (FWLS) formulation is given for identifying the parameters of Hammerstein-type nonlinear continuous-time systems (1930) based on input and noise contaminated output data observed over a finite time interval.
Abstract: A frequency weighted least squares (FWLS) formulation is given for identifying the parameters of Hammerstein-type nonlinear continuous-time systems (1930) based on input and noise contaminated output data observed over a finite time interval. The Hartley modulating functions (HMF) method (1942) starts from a priori knowledge of the Hammerstein system structure with unknown parameters. The approach converts the nonlinear differential equation describing the nonlinear system into a Hartley spectrum equation and circumvents the need to estimate unknown initial conditions through the use of certain modulation properties. The unknown system parameters can then be estimated in the frequency domain by a FWLS-algorithm. A root mean square normalized error criterion is applied to measure the bias of the estimate for different values of the mode number and order of the Hartley transformation as well as for different levels of the noise-to-signal ratio in order to investigate some computational considerations associated with the methodology. The illustrative Monte Carlo simulation studies suggest that this method lies in the potential of being able to accurately estimate the parameters of a nonlinear continuous-time Hammerstein system in the presence of significant output measurement disturbances.
15 citations
TL;DR: In this paper, the spin-lattice relaxation time (T) of individual-carbon resonances has been measured in the 3C Fourier transform NMR spectra of proteins.
Abstract: The resolution in proton-decoupled natural-abundance i3 NMRt spectra of large organic and biological molecules is normally considerably greater than in proton NMR spectra, as a result of the large range of '3C chemical shifts 'and the absence of' 3C—' 3C coupling. The Fourier transform NMR technique has partly overcome the problem of very poor sensitivity of natural-abundance l3 NMR. As examples of structural applications, 13C NMR has been used to determine the detailed anomeric composition of aqueous fructose, and to measure the extent and type of branching of various dextrans. Some problems that arise when l3( Fourier transform NMR is used for quantitative analysis are discussed. Fourier transform NMR instrumentation provides a built-in capability of measuring the spin—lattice relaxation time (T,) of individual-carbon resonances. The meaning of T, and how spin—lattice relaxation occurs are briefly discussed. Examples of T, determinations are presented. The use of T, measurements for studying rotational motions of molecules and internal rotations of sidechains is discussed. PRFT NMR spectra can be used in some cases for assigning resonances to specific carbons. The development of a probe for sample tubes of 20 mm outside diameter has increased the sensitivity of natural-abundance '3C Fourier transform nuclear magnetic resonance to the point that single-carbon resonances of proteins can be studied. Numerous narrow single-carbon resonances are observed in the aromatic region of the '3C spectrum of native hen egg-white lysozyme. Theoretical and experimental evidence shows that these narrow resonances are those of the 28 non-protonated aromatic carbons. The 59 protonated aromatic carbons give rise to a background of broad peaks. Significant chemical shift variations occur upon folding of the protein into its * Contribution No. 2613. t Abbreviations: NMR, nuclear magnetic resonance PRFT, partially relaxed Fourier transform NOE, nuclear Overhauser enhancement VLDL, very-low-density lipoprotein LDL, low-density lipoprotein HDL, high-density lipoprotein 247
15 citations