On the representation of signals by basis kernels with product argument

Cohn-Sfetcu, S.; Smith, M. R.; Nichols, S.T.

doi:10.1109/proc.1975.9745

Cited by 10 publications

(4 citation statements)

References 5 publications

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“…Cohn-Sfetcu et al proved that this method can also be used to analyze multicomponent Gaussian, Lorentzian, and (sin x )/ x type functions by using another model function kk ( x ). They 13 applied the improved GGM method for the analysis of pulsed NMR measurements.…”

Section: Methodsmentioning

confidence: 99%

“…A lot of techniques have been proposed yet to analyze multicomponent decay curves based on, e.g., graphical extraction, linear , and nonlinear (NLLS) least-squares methods, singular value decomposition, − Gardner's method, − or Prony's method. − The success of these techniques is often hampered by the ill conditioning property of the exponential-sum fitting problem. Furthermore, the final results seem to depend strongly upon the input of the correct number of exponential components and upon the initial estimates of the preexponential factors and decay constants λ i .…”

Section: Introductionmentioning

confidence: 99%

“…From the practical point of view, this method did not gain much success because at that time the numerical evaluation of the Fourier transformations was very cumbersome and tedious. After development of the fast Fourier transform (FFT) technique the method was revised by Schlesinger 10 and, independently, by Smith and Cohn-Sfetcu. − Additionally, they combined the technique with an adequate low-pass filter in order to decrease the effects of computational noise and of the high frequency noise normally present in experimental data. They also showed that the improved method of Gardner et al was able to analyze all kinds of multicomponent decay curves as long as the model functions were known.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Schreurs¹,

François²,

Adriaensens³

et al. 1999

J. Phys. Chem. B

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A combination of the methods of Gardner and Prony is used for the qualitative and quantitative analysis of solid-state free induction decay (1H NMR) curves of isotactic polypropylene, recorded at 40, 60, 80, and 100 °C at constant time intervals. These multicomponent decay curves contain information about the physicochemical structure of the polymer sample: each component is characterized by a specific model function containing a spin−spin relaxation time T 2 and an intensity as parameters depending on the properties and amount of the corresponding phase. The number of phases is still an unanswered question. Each FID curve is analyzed by using an improved method of Gardner et al. in order to reveal the number of phases, to predict the best fitted model function, and to estimate the T 2 value of each component. The quantification of the parameters (T 2 and fraction) with Prony's improved method is discussed. The presence of an intermediate phase is unambiguously demonstrated. The influence of temperature on the physicochemical structure of the polymer is examined. The precision of the computed parameters is discussed for the analyses of three consecutively measured FID curves of isotactic polypropylene at 60 °C.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Schreurs¹,

François²,

Adriaensens³

et al. 1999

J. Phys. Chem. B

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“…The Mellin transform [6] arises in the analysis of time-varying networks [7], in space-variant image restoration [8], and in the analysis of signals with multicomponents of the same form but different width [9]. Its use has also been suggested for speech processing [5 ].…”

Section: Optical Mellin Transformsmentioning

confidence: 99%

Scale invariant optical correlation using Mellin transforms

Casasent

Psaltis

1976

Optics Communications

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The use of optical Mellin transforms in matched spatial filter correlation of imagery that differs in scale is discussed. Theoretical considerations and initial experimental results are included. The intensity of the correlation peak is found to be indeigendent of the input scale, and the scale difference between the two functions to be correlated can also be extracted from the location of the correlation peak.

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Initial Parameter Guess of Free Diffusion Processes

Scavarda

1983

Control of Distributed Parameter Systems

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On the representation of signals by basis kernels with product argument

Cited by 10 publications

References 5 publications

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Scale invariant optical correlation using Mellin transforms

Initial Parameter Guess of Free Diffusion Processes

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On the representation of signals by basis kernels with product argument

Cited by 10 publications

References 5 publications

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (1H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (1H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Scale invariant optical correlation using Mellin transforms

Initial Parameter Guess of Free Diffusion Processes

Contact Info

Product

Resources

About

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study

Qualitative and Quantitative Analysis of Solid State Free Induction Decay (¹H NMR) Curves Using a Combination of the Methods of Gardner and Prony: Isotactic Polypropylene as a Case Study