We investigate synchronization in neuronal networks with a small-world-like structure. Inhibitory connected neurons are considered. In a previous study, we found an interesting quasi-periodic solution such that neurons are classified into three groups: two groups with distinct firing rates and one group with only subthreshold oscillations. In this paper, we study its generation mechanism in the smallest system in which we can reconnect one synapse. As a result, we obtain the following mechanism: (1) non-uniformity of the firing frequency appears as a result of asymmetrical coupling, (2) neurons with a higher firing frequency suppress neurons with a lower firing frequency for an appropriate coupling coefficient, (3) three clustered states, that is, neurons with firing frequencies A and B (A/B is irrational) and neurons that do not fire, are generated. We also confirm this mechanism in a large population.

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This research has proposed a novel algorithmic scheme of infinite impulse response (IIR) filter for bandwidth compensatory in digital signal processing (DSP) system based on the pole-zero placement technique. The scheme development started with the determination of the analog output or reconstruction filter gains at the zero, cut-off and Nyquist frequencies and then their respective nonlinear system equations. The Newton-Raphson method was subsequently applied for the positions of pole and zero and the gain of the output filter. The constants were re-substituted in the initial transfer function and an inversion carried out. To verify the applicability of the proposed scheme, simulations were carried out at two cut-off frequencies (i.e. 1.5 and 2kHz) and three sampling frequencies (i.e. 10, 12 and 14kHz). To further validate, experiments were undertaken whereby the algorithmic scheme was applied to a digital signal processing system. The simulation and experimental results revealed that the scheme implementation could effectively address the attenuation phenomenon, compensate the system bandwidth as well as enhance the time response of the output signal.

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We propose a new blind deconvolution algorithm taking both input and output noise into consideration. Already we have proposed a blind identification method based on a model including input and output noise. An algorithm of deconvolution, however, was not proposed. In this paper, we propose a blind deconvolution algorithm based on a model including input and output noise. The performance of the proposed deconvolution algorithm is evaluated by computer simulations.

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First, we demonstrate that the eigen-values and corresponding eigen-vectors of the cascade matrix of a lossless reciprocal circuit are the iterative parameters known in classical circuit theory. When these iterative parameters are used, conjugate impedance matching is demonstrated to be a valid matching method of circuit theory. In addition, the iterative impedances at the left and right of an asymmetric circuit are complex conjugates; hence, an impedance-matched network can be obtained by iteratively connecting the same circuits. In other words, the roles of the regularly spaced knots, which were proposed by O. Heaviside and are the bases of the lumped loading coils, are shown to be valid from the theory of iterative parameters. Networks with a periodic structure obtained by iteratively connecting the same circuits are effective for obtaining resonances and eigen-oscillations.

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