Design of Gm-C wavelet filter for on-line epileptic EEG detection

Abstract

Analog filter implementation of continuous wavelet transform is considered as a promising technique for on-line spike detection applied in wearable electroencephalogram system. This Letter proposes a novel method to construct analog wavelet base for analog wavelet filter design, in which the mathematical approximation model in frequency domain is built as an optimization problem and the genetic algorithm is used to find the global optimum resolution. Also, the Gm-C filter structure based on LC ladder simulation is employed to synthesize the obtained analog wavelet base. The Marr wavelet filter is designed as an example using SMIC 1V 0.35µm CMOS technology. Simulation results show that the proposed method can give a stable analog wavelet filter with higher approximation accuracy and excellent circuit performance, which is well suited for the design of low-frequency low-power spike detector.

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

“…To evaluate the performance of approximation method, L 2 -norm is used to quantify the fitting error between ideal Marr wavelet and constructed analog wavelet base. Noted that, as an improvement, the fitting error in this paper is measured by the magnitude of overall transfer function in frequency domain, not the denominator as used in MSA and [20]. Thus, the rational approximation of wavelet base can be regarded as an optimization problem that minimizes the L 2 -norm of the error function, i.e.…”

“…As an improvement of MSA, [20] presented a method converting rational approximation to an optimization problem, which can remove the possibility of instability. However, since the optimization objective is defined by polynomial fitting of the denominator in (6), the proposed method is still struggling in realizing an accurate approximation.…”

“…However, since the optimization objective is defined by polynomial fitting of the denominator in (6), the proposed method is still struggling in realizing an accurate approximation. Moreover, like MSA and other existing approximation methods, the time delay t 0 in [20] should be selected manually. Small t 0 will result in large truncation error and thus low similarity between ideal and approximated wavelet base, while large t 0 will increase the difficulty in approximation due to extra range remaining close to zero and thus require high-order wavelet filter with large chip size and high power consumption [18].…”

“…The proposed approximation method can be used to construct analog Marr wavelet base at arbitrary filter order. To give a detailed comparison with MSA and [20], the mathematical approximation model for constructing seventh-order Marr wavelet filter at a = 1 is taken as the example. Also, the number of sampled frequency points N is set to be 701 with dominant frequency range 0-7 rad/s covered.…”

“…Furthermore, MSA cannot guarantee the obtained analog wavelet base stable for arbitrary filter order and time delay. To overcome the problems with MSA, the approximation method using genetic algorithm has been proposed in [20]. Although successful in generating stable wavelet filter, this approach still has trouble in enhancing approximation accuracy.…”