Analysis of transient multiexponential signals using cepstral deconvolution

Abstract

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.

Transient multiexponential signals analysis using Bayesian deconvolution

“…For medium and high SNR, the maximum percentage deviation of S 1 (τ ) and S 2 (τ ) between the estimated and expected values of decay rates is 12%, which is better than cepstral deconvolution method with 133.8% in [10]. Besides, the noise is not considered in this method.…”

“…Monoexponential and biexponential signals are employed as in [10]. Both signals are widely used in fluorescence decay experiment, and each decay rate λ i in Eq.…”

“…The main disadvantage of these methods is the data length constraint. Then, Cepstral deconvolution method was proposed to eliminate the data length constraint [10]. It was fast and computationally inexpensive, but this method fell short in accurately estimating the decay rates and the influence of noise was not considered.…”

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

“…Recently, Jibia et al [7] related it to the bandwidth of the conceptual system response ) (t h by using the concept of noise equivalent bandwidth. If the NEB is given by (23) By integrating and taking the limits to be 0 and some arbitrary min t sufficiently large, they showed that the bandwidth is given by 2   B (24) For unaliased sampling, therefore, the sampling frequency,  contributes to noise reduction, it is not advisable to raise its value very high because of the deleterious effect this may have on the detectability of certain components.…”

“…This modification recently proposed by Jibia et al [7] consists of a six-step procedure to extract the input signal from the discrete deconvolution model resulting from Gardner transform. The procedure as outlined in that paper is as follows: In other words, the cepstrum is the even part of the complex cepstrum.…”