## 5 Signal Processing and Feature Computation  
Sensors often generate data with high dimensionality, therefore extracting the meaningful information of sensor signals requires effective feature computation methods. The next design step in our ADIMSS tool is to obtain the optimal combination of signal processing and feature computation from the method library and to find the best parameter settings. The method library is subject to continuous extension by manually or evolutionarily conceived algorithms. Signal Pre-processing and Enhancement (SPE) is a first stage of signal processing for noise removal, drift compensation, contrast enhancement and scaling. For example, in the particular case of gas sensor systems, the methods used in the signal prepocessing and enhancement step are differential, relative, fractional [32, 35], and derivation [33, 36]. In the framework of ADIMSS, the set of operations applied to analyze and extract the features are listed with ID number, which is included in the representation of candidate solutions of PSO or GA. The ID number is evolved in optimization process  
Figure 17: An intrinsic method of the local optimization to obtain the optimum multi-sensor and their parameters. to indicate the selected method. Table 2 presents a list of signal pre-processing and enhancement, where the method for IDSPE\(=1\) is stated as '_None_', which means that no operation of SPE will be applied. Common types of features mostly extracted from raw sensor signals are the geometric attributes of signal curve (e.g., steady state, transient, duration, slope, zero-crossings), statistical feature (mean, standard deviation, minimum, maximum, _etc._), histogram, spectral peaks (Fourier Transform), Wavelet Transform, Wigner-Ville Transform, auditory feature for sound and speech signals, _etc._ Table 3 summarizes a small list of feature computation methods. Here, two operators of heuristic feature computation (_i.e._, Multi-level thresholding and Gaussian Kernels) applied in gas sensor systems are picked up as examples to demonstrate the autoconfiguration of feature computation in the proposed ADIMSS tool. _Multi-level thresholding_ (MLT) operators are a heuristic feature computation method that extracts the features by counting samples of signal responses lying in the range between two thresholds. MLT is derived from histogram and amplitude distribution computation by non-equal range of bins [15]. Figure 18 illustrates differential and cumulative (up and down) modes of MLT computation. The MLT is optimized by moving of the levels up and down until the optimal solution with regard to the classification rates and other assessment criteria achieved. The number of features extracted by MLT depends on the number of thresholdings minus one. In the optimization process, the numbers of thresholds are swept from 3 to 10 (the maximum number of thresholds can be defined by designer) and \begin{table}
\begin{tabular}{c l l} \hline \multicolumn{1}{c}{**IDSPE**} & \multicolumn{1}{c}{**Method**} & \multicolumn{1}{c}{**Equation**} \\ \hline
1 & None & \(\cdots\) \\
2 & Differential & \(h(t)=\big{(}s(t)+\delta_{a}\big{)}-\big{(}s(0)+\delta_{a}\big{)}=s(t)-s(0)\) \\
3 & Relative & \(h(t)=\dfrac{s(t)\big{(}1+\delta_{a}\big{)}}{s(0)\big{(}1+\delta_{a}\big{)}}= \dfrac{s(t)}{s(0)}\) \\
4 & Fractional & \(h(t)=\dfrac{s(t)-s(0)}{s(0)}\) \\
5 & Derivation & \(h(t)=s(t)-s(t-1)\) \\ \hline \end{tabular}
\end{table} 
Table 2: List of signal pre-processing and enhancement methods used for gas sensor systems filled in the design tool of ADIMSS. \begin{table}
\begin{tabular}{l l l} \hline \multicolumn{1}{c}{**IDFC**} & \multicolumn{1}{c}{**Method**} & \multicolumn{1}{c}{**Parameter**} \\ \hline
1 & Steady-state & none \\
2 & Transient integral & none \\
3 & Histogram & range of bins, down\_bnd, up\_bnd \\
4 & MLT & thresholds (\(T_{L}\)); \(L=1\), 2, \(\ldots\), n \\
5 & GWF & \(\mu_{b}\), \(\sigma_{b}\), \(M_{b}\); \(k=1\), 2, \(\ldots\), n \\
6 & Spectral peaks (FFT) & None \\ \hline \end{tabular}
\end{table}