# An Overview of IoT Sensor Data Processing, Fusion, and Analysis Techniques
## 3 IoT Sensor Data Processing
### Denoising  
The voluminous sensor data generated in the IoT network needs data analysis, mostly with real-time decision-making. The characteristics of sensor data are complex, involving high velocities, huge volumes, and dynamic values and types. Further, the sensor data pollute while perpetuating numerous obstacles until producing the required data analysis and real-time decision-making. Noise is an uncorrelated signal component that enacts unwanted change and modification on the original vectors of the signal. The noise feature leads to the unnecessary processing and utilization of resources for handling the unusable data. The wavelet transform methods are capable of representing the signal and addressing the problem of signal estimation effectively. Significantly, the wavelet transformation preserves the original signal coefficients by removing the noise within the signal. This is achieved by thresholding the coefficient of noise signals, hence the perfect thresholding scheme is essential. The wavelet transformation is a prevalent method to analyze and synthesize continuous-time signal energy. Let \(e(t)\), \(t\in\mathrm{R}\) represent the signal energy, while it must satisfy the constraint defined as  
\[||e||^{2}=\int_{-\infty}^{\infty}\bigl{|}e(t)\bigr{|}^{2}dt<\infty, \tag{1}\]  
where the signal energy \(e(t)\) that satisfies the constraint in Equation (1) belongs to the squared search space \(L^{2}(R)\). The wavelet transformation is also used to analyze the discrete-time signal energy and eliminate the noise with energy signals. The wavelet transformation method allows us to investigate the signal characteristic by zooming at different time scales. The experimental results exhibited significant improvements in denoising the sensor signals. There are two types of wavelet transforms, namely Continuous Wavelet Transform (CWT), which targets signal analysis on a time-frequency level, and Discrete Wavelet Transform (DWT) that targets signal analysis a time level. Continuous Wavelet Transform (CWT)In CWT, the signal energy \(e(t)\) is represented using a set of wavelet functions \(C=\left\{W_{\psi}(\alpha,\beta)\right\}\), \(\alpha\in R^{+};\beta\in R\), where \(\alpha\) represents the dilation scaling factor, and \(\beta\) represents the shifting time localization factor, while \(\psi\) represents the wavelet function. The wavelet coefficient on the time-frequency plane is given by Equation (2). \[W_{\psi}(\alpha,\beta)=\int_{-\infty}^{\infty}\frac{1}{\sqrt{\alpha}}\psi_{0} \biggl{(}\frac{\lambda-\beta}{\alpha}\biggr{)}e(\lambda)d\lambda \tag{2}\]  
where \(\psi_{0}\) represents the shifted and dilated form of the original wavelet \(\psi_{0}(t)\). The CWT is a function controlled by two parameters. The CWT targets to find the coefficients of the original signal \(e(t)\) based on the shifting factor (\(\beta\)) and the dilation factor (\(\alpha\)). Discrete Wavelet Transformation (DWT)The DWT for continuous-time signals refers to transforming signals performed upon a discrete-time signal. The coefficients obtained from this transformationare defined in subset \(D=W_{\psi}(\mathcal{D}^{\alpha},\mathcal{D}^{\alpha}\beta),\alpha\in\mathbb{Z},\ \beta\in \mathbb{Z}\). For a given continuous-time signal \(e(\lambda)\), the coefficients of DWT are obtained using the integration of the subset D, as defined in Equation (3). \[w(\alpha,\beta)=\left(\psi_{0(\mathcal{D}^{\alpha},\mathcal{D}^{\alpha}\beta)},\ e\right)=\int_{-\infty}^{\infty}2^{-\alpha/2}\psi_{0}{}^{\prime}(2^{- \alpha}\lambda-\beta)e(\lambda)d\lambda \tag{3}\]  
where \(\alpha\) indicates the scale factor and \(\beta\) indicates the localization factor. It is to be noted that this involves continuous-time signal \(e(\lambda)\), and not the discrete signal. The authors in [24] discuss that in some instances the signals received from the IoT sensor devices have a reasonable ratio value of Signal to Noise (SNR), but are unable to achieve the required Bit Error Rate (BER).