Realization of Analog Wavelet Filter Using Hybrid Genetic Algorithm for On-Line Epileptic Event Detection

Abstract

As the evolution of traditional electroencephalogram (EEG) monitoring unit for epilepsy diagnosis, wearable ambulatory EEG (WAEEG) system transmits EEG data wirelessly, and can be made miniaturized, discrete and social acceptable. To prolong the battery lifetime, analog wavelet filter is used for epileptic event detection in WAEEG system to achieve on-line data reduction. For mapping continuous wavelet transform to analog filter implementation with low-power consumption and high approximation accuracy, this paper proposes a novel approximation method to construct the wavelet base in analog domain, in which the approximation process in frequency domain is considered as an optimization problem by building a mathematical model with only one term in the numerator. The hybrid genetic algorithm consisting of genetic algorithm and quasi-Newton method is employed to find the globally optimum solution, taking required stability into account. Experiment results show that the proposed method can give a stable analog wavelet base with simple structure and higher approximation accuracy compared with existing method, leading to a better spike detection accuracy. The fourth-order Marr wavelet filter is designed as an example using Gm-C filter structure based on LC ladder simulation, whose power consumption is only 33.4 pW at 2.1Hz. Simulation results show that the design method can be used to facilitate low power and small volume implementation of on-line epileptic event detector.

General rational approximation of Gaussian wavelet series and continuous‐time gm‐C filter implementation

“…The approximation MSE based on different algorithms is shown in Table 2. From the comparisons, the QDE algorithm is more accurate than the improved Maclaurin method, 17 DE, and L 2 algorithms. Compared with the QDE and DE algorithms, the L 2 algorithm has the simplest computation process.…”

“…According to the above steps of the QDE algorithm, the accurate global optimal solution k i of the fifth‐order approximation h ( t ) is obtained in Table 1. The transfer functions of first‐order derivative of Gaussian wavelet filter (scale σ = 1) resulting from this approximation is obtained as The approximated Gaussian wavelets using the improved Maclaurin method, 17 L 2 , DE, and QDE algorithms are shown in Figure 3. Among them, because the improved Maclaurin method 17 is a frequency domain method, the approximation result needs to be transformed into the time domain.…”

“…However, one disadvantage of the L 2 algorithm is that the computational accuracy is affected by the initial value, so it is difficult to select the initial value of the optimal solution. Obviously, the improved Maclaurin method 17 has the lowest time domain approximation accuracy because it only approximates the denominator of the transfer function in frequency domain. The main advantage of this algorithm is that the numerator of the obtained transfer function has only one term, and the feed‐forward path in the multiloop feedback network will be relatively simple.…”

“…Among them, the time domain approximation method mainly includes L 2 approximation 11 and optimal algorithm approximation 12–14 . The frequency domain approximations are Padé, 5 Maclaurin, 6,15,16 and improved Maclaurin method 17 . In general, the time domain approximation method is more accurate than the frequency domain method because the fundamental expression of the wavelet is a time domain function.…”

“…In addition, for the wavelet filter circuit design, some circuit design methods based on different structures such as cascade and multiple loop feedback prototype, and the basic building blocks such as log domain, 5,12 switched current (SI), 13,14 switched capacitor (SC), 18 current mirror, 19 and operational transconductance amplifier (OTA; i.e. g m ), 4,15–17 are proposed. Furthermore, for analog filter design, besides the basic blocks mentioned above, there are many other basic building blocks that can be selected such as current conveyor, 20 source follower, 21,22 and complementary metal–oxide–semiconductor (CMOS) mixed integrator 23,24 .…”