**4. Signal processing approaches**

The signal processing steps in BCI are signal acquisition, preprocessing, feature extraction, feature selection, feature classification, and postprocessing. The common classification approaches in hybrid BCI are briefly discussed here.

#### **4.1. Fast Fourier transform (FFT)**

FFT is an efficient algorithm for calculation of DFT reducing order of *N*<sup>2</sup> operations to *<sup>N</sup>* log2 *<sup>N</sup>* that decomposes signal from time domain to its individual frequency components whose pairs are given as [75]:

$$X(k) = \sum\_{\mathbf{n}=0}^{M-1} x(\mathbf{n}) \text{ W}\_{\mathbf{N}}^{\text{tu}} \tag{1}$$

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$$\mathbf{x}(n) = \frac{1}{N} \sum\_{k=0}^{N-1} \mathbf{X}(k) \,\mathrm{W}\_N^{-kn} \tag{2}$$

where *WN* <sup>=</sup> *<sup>e</sup>* <sup>−</sup>*<sup>j</sup>* ( \_\_\_ 2*π <sup>N</sup>* ) and N = length [*x(n)*].

The selection of a target based on hybrid P300-MI BCI was developed by [72] on 1166×721 pixels monitor using two sequential tasks: cursor movement with the help of ERD from left-/right-hand movement imaginations and selection/rejection of the target from focused attention on flashing to evoke P300 keeping one system passive when other is active. Eleven healthy subjects (10 male, 1 female subjects, and age 22–32 years) were used in both online and offline analysis and each experiment was performed within 2 s with each trial duration for about 18 s. Two targets such as Green Square for selection and Blue Square for rejection were randomly appeared on the screen and the classification accuracy was about 93% in real

MI-based brain switch was merged with P300 sequentially by [73] in which right-/left-hand movement imaginations was used for control signal acting as a brain switch to turn ON/OFF P300 speller. Eleven healthy subjects (8 male, 3 female subjects, and age 23–30 years), with a few subjects having previous experience to P300 or MI, were experimented. Offline training was done for P300 and MI before real tests in a 22″ LED monitor containing 6×7 matrix of 26 English letters, 10 numbers, a few special characters, and commands. SWLDA was used for P300 classification and filtration in the alpha-beta rhythm range with two bands discrimination using CSP for MI and the classification accuracy achieved was about 92% for P300.

An efficient approach was proposed by [74] combining MI with P300 in a block diagonal matrix form to improve classification accuracy concatenating features of each paradigm where first-order information was used for P300 and second order for MI. Twelve volunteers (10 male, 2 female subjects, age 22–35 years) were experimented provided with eight flashing buttons and an arrow cue such that screen remained blank for initial 2.25 s and a cross appeared on the screen from 2.25 to 4 s to attract subject's visual attention. Arrow cue was displayed from 4 to 8 s such that up arrow was for P300 task to focus on the random flashing buttons without MI tasks and right arrow for MI task to make left-/right-hand imaginations. Test data was obtained from second experimental session and the classification accuracy was

The signal processing steps in BCI are signal acquisition, preprocessing, feature extraction, feature selection, feature classification, and postprocessing. The common classification

that decomposes signal from time domain to its individual frequency components whose

*n*=0 *N*−1

*x*(*n*) *WN*

operations to *<sup>N</sup>* log2 *<sup>N</sup>*

*kn* (1)

time.

about 92%.

**4. Signal processing approaches**

126 Evolving BCI Therapy - Engaging Brain State Dynamics

**4.1. Fast Fourier transform (FFT)**

pairs are given as [75]:

approaches in hybrid BCI are briefly discussed here.

*X*(*k*) = ∑

FFT is an efficient algorithm for calculation of DFT reducing order of *N*<sup>2</sup>

Amplitude vs. frequency is plotted and the dominant amplitude at a particular frequency is obtained for SSVEP signal analysis in BCI. FFT classifier has been replaced by other better classifiers in BCI research.

#### **4.2. Linear discriminant analysis (LDA)**

LDA, also known as Fisher's LDA (FLDA), is a useful classification technique that transforms features into a low-dimensional space with high degree of separation. Suppose, there are a certain set of samples belonging to classes "A" and "B" whose mean and scatterings within each classes are represented as *μA* , *μB* and *SA* 2 , *SB* 2 , respectively, and LDA is calculated as [76].

$$LDA = \frac{(\mu\_A - \mu\_b)^2}{S\_A^2 + S\_b^2} \tag{3}$$

This method is simple to use, has low computational cost with high accuracy, and is widely used in number of BCI applications for P300 and MI-related tasks [77]; but, it also suffers from small sample size and linearity problems [78]. BLDA, a Bayesian version of LDA, is useful for P300 in which parameters are estimated with Bayesian regression whose probabilistic output value lies between zero and one. It gives good results for small number of train sets or noise contaminated data and may give poor result for a complex nonlinear EEG data [78, 79]. SWLDA is a stepwise LDA that performs space reduction by selecting suitable features and stepwise analysis to remove least significant features which is an effective classification technique for online classification of P300 [80].

#### **4.3. Support vector machine (SVM)**

SVM is used for classification of linearly separable binary data sets that uses a discriminant hyperplane to identify classes and the best choice is the hyperplane that leaves maximum margin from both classes. The kernel generally used in P300 BCI is the Gaussian kernel and the corresponding SVM is Gaussian SVM which is given as:

$$\mathbf{K}(\mathbf{x}, \mathbf{y}) = \exp\left(\frac{-\left\|\mathbf{x} - \mathbf{y}\right\|^2}{2\sigma^2}\right) \tag{4}$$

where K(x, y) is kernel function and σ is kernel width.

SVM is simple and stable, and has a low variance which may be a key for low classification error for unstable and noisy P300 signals. SVM produces good results with high-dimension feature vectors and a small training set, thus outperforming LDA, but are generally slower than other classifiers [79]. BLDA is most robust for P300 application compared with LDA and SVM [81].

### **4.4. Canonical correlation analysis (CCA)**

CCA is a multivariate statistical method to analyze frequency components of SSVEP in EEG [82]. It extracts narrowband frequency components of SSVEP in EEG using maximum correlation between reference stimulus signals and EEG signals. Suppose X be the EEG all channels data and *Yf* be the reference signals at f Hz stimulus frequency with N number of harmonics, the reference signals *Yf* are given as:

$$Y\_f = \begin{pmatrix} \sin(2\pi ft) \\ \cos(2\pi ft) \\ \vdots \\ \sin(2\pi Nft) \\ \sin(2\pi Nft) \\ \cos(2\pi Nft) \end{pmatrix} \tag{5}$$

The maximum correlation among X and *Yf* is obtained as:

$$\rho\_{\text{max}} = \max\left[\text{correlation coefficient } (\mathbf{X}, \mathbf{Y})\right] \tag{6}$$

CCA is more common method for analysis of SSVEP signals in frequency domain that improves SNR, classification accuracy, and ITR [81, 83].

#### **4.5. Common spatial patterns (CSPs)**

CSP is used to analyze spatial patterns of MI calculating spatial filters to find optimum variances for two different classes of EEG data. It uses simultaneous diagonalization of two covariance matrices, and the spatially filtered signal Z of a single-trial EEG data is obtained as:

$$\mathbf{Z} = \mathbf{W}\mathbf{E}\tag{7}$$

applications include use of computer and communication, prosthetics using artificial limbs, advanced functional electrical therapy, monitoring ALS patients, entertainment and care in virtual smart home where MI is used mostly in prosthetics. Although BCI application is

**Application type Specific control Hybrid type References** Wheelchair Direction P300 + MI [50]

Computer cursor 2-D SSVEP + MI [52, 90]

Speller Spelling accuracy P300 + SSVEP [55, 68]

Artificial limb Upper limb SSVEP + MI [62, 64]

Functional electrical therapy Advanced SSVEP + MI [66] ALS patients Communication P300 + MI [92]

Virtual environment Smart home P300 + SSVEP [94, 95]

"Go" and "Stop" movement P300 + SSVEP [54] Speed SSVEP + MI [65] Multi-degree SSVEP + MI [86] Speed and direction SSVEP + MI [63]

Autonomous navigation P300 + MI [89]

Multidimensional robotic arm [91]

Awareness P300 + SSVEP [93]

Intelligent nursing bed [96]

P300 + MI [87, 88]

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P300 + MI [72]

P300 + MI [71, 73]

Phenomenon of acquiring and processing information by human brain is still unknown. A very few hybrid BCI are experimented with target users and most of the subjects are healthy with small sample size. Rehabilitation using BCI is still not used in clinical practice [97]. Various methods have been incorporated to improve accuracy and ITR, and some hybrid with different classifiers combination have shown some improved results, but mostly subject's specific. Type and design of electrodes have impact on subject's head which influence EEG signals and demands for high compatible systems. These systems are not free from physical and mental fatigue that challenges their adaptability. Moreover, there are obstacles

potentially safe, it needs regulatory approval before the experiment.

**6. Limitations**

**Table 2.** Hybrid BCI applications.

where E is *N* × *T* matrix of single-trial raw EEG data, N is the number of channels, T is the number of measurement samples per channel, and W is CSP projection matrix. The rows of W are stationary spatial filters and the columns of *W*−1 are common spatial patterns. Spatial patterns of motor action are dependent on the specific region of brain like left-hand movement on right cerebral hemisphere [84]. A higher classification accuracy for multitask learning with very few training samples among 19 healthy subjects was achieved by [85] in which spatial filter was replaced by Laplacian filter in CSP algorithm.
