Fit to experimental data with exponential functions using the fast fourier transform

Schlesinger, J.

doi:10.1016/0029-554x(73)90314-5

Cited by 41 publications

(7 citation statements)

References 2 publications

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“…The discrete form of (4) was obtained by selecting t = 0.25, n max = 20, n min = −107 making N = 128. Values of ξ , N 0 and γ were experimentally selected to be 0.94, 20 and 0.8 respectively.…”

Section: Tablementioning

confidence: 99%

“…The difficulty at that time was the nonavailability of effective algorithms for the computation of Fourier integrals. This problem was solved later by Schlesinger [4] using the fast Fourier transform (FFT). Nichols et al [5] further modified the Gardners' transformation by introducing a weighting factor, α, in the nonlinear transformation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of transient multiexponential signals using cepstral deconvolution

Jibia

Salami

Khalifa

et al. 2010

Applied and Computational Harmonic Analysis

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We propose and test a new method of multiexponential transient signal analysis. The method based on cepstral deconvolution is fast and computationally inexpensive. The multiexponential signal is initially converted to a deconvolution model using Gardners' transformation after which the proposed method is used to deconvolve the data. Simulation and experimental results indicate that this method is good for determining the number of components but performs poorly in accurately estimating the decay rates. Influence of noise is not considered in this paper.

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Section: Tablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of transient multiexponential signals using cepstral deconvolution

Jibia

Salami

Khalifa

et al. 2010

Applied and Computational Harmonic Analysis

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“…Realizing this shortcoming, Schlesinger proposed a means of alleviating it. His proposal published in [3] consists of the replacement of the numerical integration of the Fourier transform and its inverse with the discrete Fourier transform and its fast Fourier transform algorithm of Cooley and Tukey [8].…”

Section: A Schlesinger's Fft Techniquementioning

confidence: 99%

“…Gardner transform belongs to the more general class of spectroscopic methods [2] in which the decay is described by a continuous distribution of decay rates which may be considered as a spectral representation of the transient signal At the time it was introduced, Gardner transform did not attract the attention of many researchers basically because of the nonavailability of effective algorithms for the computation of Fourier integrals. This problem was later solved by Schlesinger [3] using the fast Fourier transform (FFT). Although successful in simplifying the numerical computation of the Fourier integrals, Schlesinger's method did not have a good filtering technique to eliminate the side ripples caused by FFT and noise.…”

Section: Introductionmentioning

confidence: 99%

An Appraisal of Gardner Transform-Based Methods of Transient Multiexponential Signal Analysis

Jibia¹,

Salami²

2012

IJCTE

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Abstract-There are several problems in applied science in which experimental observations can be accurately represented by a sum of exponential decay functions in which the amplitudes, decay rates and number of components have different physical interpretations and need to be estimated. A parameter estimation technique of multicomponent exponential functions that has undergone many modifications is the Gardner transform in which a nonlinear transformation is used to convert the data signal into a convolution model containing the parameters of interest. Modifications of this early technique include modification of the original transform or deconvolution procedure and additional processing of the deconvolved data to obtain better estimates of the desired parameters. This paper presents an appraisal of Gardner transform and its variants. It discusses major modifications and their implications to the overall results of analysis.

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“…However, the algorithm is time-consuming in the computation of Fourier integrals and the error ripples may blur the real peaks of the spectrum. These problems were improved significantly with fast Fourier transform (FFT) technique proposed by Schlesinger et al [6,7]. However, the length of deconvolved data had limitation in order to avoid the high-frequency noise for deconvolving with inverse filtering.…”

Section: Introductionmentioning

confidence: 98%