Integration of DWT, FFT, and Spatial domain for the identification of epileptic seizure utilizing electroencephalogram signal

FFT can be applied to different fields due to its inherent nature. A mathematical tool called FFT is used to translate waveform data from the time domain into the frequency domain [25–26]. The signal that has been analyzed is shown as a succession of sinusoids in the FFT. The “Discrete Fourier Transform (DFT)” is far slower than FFT. With FFT, the presence of various frequencies and, in turn, their magnitudes, may be retrieved. Both discrete and continuous time domains can be used for FT. In real time, FT of a function z(t) is Z(ω), where, [1, 2] (1) Zω=∫−∞∞zte−jωtdt Z\left( \omega \right) = \int_{ - \infty }^\infty {z\left( t \right){e^{ - j\omega t}}dt} where J=−1 J = \sqrt { - 1} and ω is the frequency. FT inverse of Z(ω) is z(t), which can be written as (2) zt=12π∫−∞∞Zωejωtdt z\left( t \right) = {1 \over {2\pi }}\int_{ - \infty }^\infty {Z\left( \omega \right){e^{j\omega t}}dt} where Z(ω) indicates signal’s spectrum. Discrete domain signal z(n), the DFT is, (3) Zl=∑n=1N−1zne−2πjln/N;0≤l≤N−1 Z\left( l \right) = \sum\nolimits_{n = 1}^{N - 1} {z\left( n \right){e^{ - 2\pi jln /N}}} ;0 \le l \le N - 1

N indicates the number of samples and n = 0, 1, 2, …, N-1. Eq. (3) is known as the N-point DFT. The FFT algorithm, which reduces the evaluation time and complexity of DFT, was proposed by Cooley and Tukey in 1965. Two basic methods used for calculating the FFT are the decimation in time (DIT) and decimation in frequency (DIF) algorithms. They vary in how they break down the problem and handle the input. DIT essentially performs DIT domain by recursively splitting the input signal into smaller sequences according to even and odd time indices. This indicates that the DIT algorithm computes the output in natural frequency order after starting with the input sequence in bit-reversed order. Following the initial arithmetic operations in each stage, the butterfly operations in DIT apply the twiddle factors. By breaking down the output spectrum into even and odd frequency components, DIF, on the other hand, operates in the frequency domain.

Although it generates the output in bit-reversed order, it processes the incoming data in normal order. Triggered factors are applied before butterfly operations in DIF. Despite the same computational complexity, the two algorithms differ in their structure and functionality. For input-side optimization, DIT is frequently more straightforward, but DIF might be better when the final output needs to be in natural order. Both methods produce the same FFT output in spite of these structural variations, and are selected according to hardware limitations or implementation preferences.

While N/2 log2N complex multiplication is needed to calculate FFT, the total number of N2 complex multiplications is needed to compute “N” point DFT. These represent FFT’s dominance over DFT. In our proposed method, we have used the DIF algorithm. Figure 6 shows the samples of the EEG signal after application of the FFT for 5 different classes of the used dataset.

WT is used to obtain a better time-frequency representation of a signal. For the local representation of non-stationary signals, this mathematical method is employed. WT is separated into two categories: CWT and DWT. Compared to DWT, CWT has far higher computational complexity and generates a lot more data. To extract the frequency information from the signal, a high-pass filter (HPF) and a low-pass filter (LPF) are applied to the signal at each level in the DWT. The output of the LPF is known as approximation or approximate coefficients, which contain lower-order harmonics of the studied signal, and the output of the HPF is known as detail coefficients, which contain higher-order harmonics. Both approximation coefficients (from low-pass filtering) and detail coefficients (from high-pass filtering) are important yet different in DWT-based EEG feature extraction. Their contributions stem from their capacity to depict various frequency components of the EEG signal, which is multi-frequency and intrinsically non-stationary. In this work, we have used approximation coefficients from the first-level decomposition, represented as A1.

The degree of decomposition in DWT analysis is determined by the frequency information needs for the study. “db4” is regarded as the mother wavelet in this work. Although various mother wavelets have also been tested for this purpose, “db4” is the most appropriate in this case for the study. The approximation coefficients (zlow[n]) and detail coefficients (zhigh[n]) in DWT analysis are computed at each decomposition level using the formula shown below [39, 40]. (4) zlown=∑k=−∞∞yk v2n−k {z_{low}}\left[ n \right] = \sum\limits_{k = - \infty }^\infty {y\left[ k \right]\;v\left[ {2n - k} \right]} (5) zhighn=∑k=−∞∞yk w2n−k {z_{high}}\left[ n \right] = \sum\limits_{k = - \infty }^\infty {y\left[ k \right]\;w\left[ {2n - k} \right]} where y is the signal that has been evaluated, k is the number of samples, n is the number of decomposition levels, and v and w are the outputs of the low pass and HPFs, respectively. The frequency range of approximation and detail coefficients can be computed using the following formulas. (6) UCA=0, 2−l−1fs {U_{CA}} = \left[ {0,\;{2^{ - l - 1}}{f_s}} \right] (7) UCD= 2−l−1fs, 2−l fs {U_{CD}} = \left[ {\;{2^{ - l - 1}}{f_s},\;\;{2^{ - l}}\;\;{f_s}} \right] where l is DWT decomposition level and f is sampling frequency. Samples of A1 (Approximation Coefficients) after applying DWT of 5 different classes are depicted in Figure 5.

In DWT analysis, the analyzed signal is decomposed at every decomposition level, from where approximation and detail coefficients are extracted. Approximation coefficients consist of lower-order harmonics, whereas detail coefficients consist of higher-order harmonics. Figure 2 depicts DWT decomposition up to decomposition level two (2) though decomposition can be done up to any level, where l is DWT decomposition level and f is sampling frequency. Samples of A1 (Approximation Coefficients) after applying DWT of 5 different classes are depicted in Figure 5.

Figure 2:

DWT decomposition up to level two (2). DWT, discrete wavelet transform; EEG, electroencephalogram.

In this model as depicted in Figure 1, EEG signals are first pre-processed. Clean EEG signal extraction from a corrupted EEG signal is known as denoising. Savitzky–Golay (SG) finite impulse response (FIR) filter is used here for denoising the EEG signal. In this filter, successive data points are fitted with a low polynomial degree to smooth the noisy signal. In the SG filter, high-frequency components remain unaltered in their fundamental characteristics. After denoising, EEG signal has been further processed to extract different frequency information by the DIF algorithm-based FFT and DWT.

The samples of EEG signals, of 5 different classes, are depicted in Figure 3. In the next step a DWT has been applied by varying the mother wavelets. DWT divides the pre-processed EEG signal into two sub-bands. The first one is the approximation (A1) coefficients, and another is the detail coefficients (D1). Here, A1 coefficients are utilized for the next step, as shown in Figure 4. On the other hand, FFT has been applied to the pre-processed EEG signal. FFT coefficients are depicted in Figure 5.

Figure 3:

Samples of EEG signals of 5 different classes. EEG, electroencephalogram.

Figure 4:

Samples of A1 after applying DWT of 5 different classes. DWT, discrete wavelet transform.

Figure 5:

Samples of EEG signal after application of FFT for 5 different classes. EEG, electroencephalogram; FFT, fast Fourier transform.

After that, A1, FFT coefficients, and pre-processed spatial domain signals are combined. On this combined signal, then PCA and LDA have been applied separately. At the last step, three different classifiers are applied to compute the performance. Here, all the classifiers are applied to compute the importance of combined features.

Here we have calculated the categorization accuracy for three distinct scenarios. In case 1, machine learning-based classification algorithms are first calculated on the combined coefficients (A1 + FFT + spatial), and in case 2, PCA is applied to the combined coefficients to lower the dimension before the performance is calculated. In instance 3, the combined coefficients have been subjected to LDA, another dimensionality reduction technique, and the performance of various classifiers is assessed.

The actual dataset consists of 5 folders, and each folder contains 100 files of a single subject. Every file consists of an EEG recording of 23.6 sec. These time series data points are sampled into data points of length 4097 [23]. Since the data points are shuffled and sub-parts into 23 chunks. So, all chunks contain 178 data points. Among 5 folders, first one is for seizure activity, the second one contains the recording of the EEG signal which is extracted from where the tumor was located, and the third one is for the EEG signal which is recorded from a healthy area of the brain, the fourth folder contains the EEG signal which is recorded when the patient’s eyes were closed and the last one recorded when patients’ eyes were open. Here, only folder 1 contains the EEG recording of epileptic seizure. Here we have performed binary classification, namely class 1 non-seizure and class 2 seizure.

The frequency with which a machine learning model correctly predicts the result is measured by its accuracy. By dividing the total number of predictions by the number of correct predictions, accuracy can be computed. The accuracy can be expressed as a percentage or on a 0–1 scale. The better, the higher the accuracy. Achieving a perfect accuracy of 1.0 requires that each prediction made by the model be accurate. This metric is easy to compute and comprehend. The ability of the model to accurately classify data points is reflected in the intuitive perception of accuracy that almost everyone possesses.

The accuracy is defined as, (8) Accuracy=Correct PredictionsAll Predictions {\rm{Accuracy}} = {{Correct\;Predictions} \over {All\;Predictions}}

The proposed method is simulated by Colab, which is based on the Python programming environment. The number of samples for the non-seizure class is 9200, and for the seizure class is 2300, as depicted in Figure 6.

Figure 6:

Bar chart of total number of samples non-seizure and seizure.

Performance measures for the three different models are depicted in Tables 1–3, considering the 10-fold CV technique.

In this section, results are computed for two-class or binary classification (Epileptic or non- Epileptic). For all the cases, accuracy, precision, Recall, and F-measure are computed for two classes. In the case of DWT, the Daubechies wavelet (db1) has been used to decompose the signal. It is evident from Tables 1–3 that PCA performs well for the combined characteristics and has the highest accuracy of 99% only for 10 principal components. It is also noted that the combination of (spatial domain + FFT + DWT + PCA) produced the best performance for the LR classifier compared to other performance metrics like accuracy recall and F1-Score. This method yields a F1-score of 0.98, a precision value of 0.99, and a recall of 0.97.

Table 4 provides a comparative study with other state-of-the-art epilepsy detection techniques. From Table 4, it is clear that the proposed technique is better compared to Jaiswal and Banka [43], Wang et al. [44], and Shiva Shankar et al. [45]. But recognition accuracy is the same as [41, 42]. It is also observed that our technique is better compared to all other techniques due to its low feature dimension.