**1. Introduction**

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Capacitor Feedback DACs. IEEE Trans. Circuits Syst. 58: 309–318.

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> Multiexponential transient signals are particularly important due to their occurrences in many natural phenomena and human applications. For instance, it is important in the study of nuclear magnetic resonance (NMR) in medical diagnosis (Cohn-Sfetcu et al., 1975)), relaxation kinetics of cooperative conformational changes in biopolymers (Provencher, 1976), solving system identification problems in control and communication engineering (Prost and Guotte, 1982), fluorescence decay of proteins (Karrakchou et al., 1992), fluorescence decay analysis (Lakowicz, 1999). Several research work have been reported on the analysis of multicomponent transient signals following the pioneer work of Prony in 1795 (Prony, 1975) and Gardner et al. in 1959 (Gardner, 1979). Detailed review of several techniques for multicomponent transient signals' analysis was recently reported in (Jibia, 2010).

> Generally, a multiexponential transient signal is represented by a linear combination of exponentials of the form

$$S(\tau) = \sum\_{k}^{M} A\_{k} \exp(-\mathcal{A}\_{k}\tau) + n(\tau) \tag{1}$$

where *M* is the number of components, *Ak* and *<sup>k</sup>* respectively represent the amplitude and real-valued decay rate constants of the *k*th component and *n*() is the additive white Gaussian noise with variance *n2*. The exponentials in equation (1) are assumed to be separable and unrelated. That is, none of the components is produced from the decay of another component. Therefore, in determination of the signal parameters, *M*, *Ak* and *<sup>k</sup>* from

© 2012 Salami et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Salami et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

equation (1), it is not sufficient that equation (1) approximates data accurately; it is also important that these parameters are accurately estimated.

There are many problems associated with the analysis of transient signals of the form given in equation (1) due to the nonorthogonal nature of the exponential function. These problems include incorrect detection of the peaks, poor resolution of the estimated decay and inaccurate results for contaminated or closely-related decay rate data as reported in (Salami et.al., 1985). These problems become increasingly difficult when the level of noise is high. Although Gardner transform eliminated the nonorthogonality problem, it introduced error ripples due to short data record and nonstationarity of the preprocessed data. Apart from these problems, analysis of multiexponential signal is computationally intensive and requires efficient tools for its development and implementation in real-time.

To overcome these problems, modification of Gardner transform has been proposed recently with Multiple Signal Classification (MUSIC) superposition modeling technique (Jibia et al., 2008); with minimum norm modeling technique (Jibia and Salami, 2007), with homomorphic deconvolution, with eigenvalues decomposition techniques, and the Singular Value Decomposition (SVD) based-Autoregressive Moving Average (ARMA) modeling techniques (Salami and Sidek, 2000; Jibia, 2009). As reported in (Jibia, 2009), performance comparison of these four modeling techniques has been investigated. Though, all the four techniques were able to provide satisfactory performances at medium and high signal-to-noise ratio (SNR), the SVD-ARMA was reported to have the highest resolution, especially at low SNR.

Hence, the development of SVD-ARMA based algorithm for multiexponential signal analysis using MATLAB software package is examined in this chapter.

MATLAB provides computational efficient platform for the analysis and simulation of complex models and algorithms. In addition, with the aid of inbuilt embedded MATLAB Simulink block, it offers a tool for the integration of developed algorithm/model in an embedded application with little programming efforts as compared to the use of other programming languages (Mathworks, 2008). This functionality is explored in integrating the developed MATLAB-based algorithm into National Instrument (NI) Labview embedded programming tool. Hence, an integrated MATLAB-Labview software interface is proposed for real-time deployment of the algorithm. To this end, the analytical strength of MATLAB together with simplicity and user-friendly benefits of the National Instrument (NI), Labview design platforms are explored in developing an efficient, user-friendly algorithm for the real-time analysis of multiexponential transient signal.

The rest of the chapter is organized as follows. Section 2 provides brief review of techniques for multiexponential signal analysis. The MATLAB algorithm development for the signal analysis is presented in section 3. The development of an integrated MATLAB-Labview realtime software interface is then examined in section 4. Section 5 presents sample real-time data collection together with results and analysis. The chapter is concluded in section 6 with recommendation for future study.
