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The design of finite-impulse response (FIR) filters can be performed by using neural networks by formulating the objective function to a Lyapunov energy function. Focusing on this goal, the authors present an improved structure of a feedback neural network to implement the least-squares design of FIR filters. In addition to using the closed-form expressions for the synaptic weight matrix and the bias parameter of the Hopfield neural network (HNN), the proposed approach can achieve a notable reduction both in the amount of computation required and hardware complexity compared to the previous neural-based method. Simulation results indicate the effectiveness of the proposed approach. Index Terms--Closed form, finite-impulse response (FIR) filters, Hopfield neural network (HNN), least squares.

An efficient and yet simple neural-based approach is utilized to design real finite-impulse response filters with arbitrary complex frequency responses in the least-squares sense. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. To achieve good convergences for large filter lengths, a cooling process of simulated annealing is used for the neural activation function. Several examples and comparisons to the existing methods are presented to illustrate the effectiveness and flexibility of the neural-based method. Index Terms--Finite-impulse response (FIR) filter, Lyapunov energy function, neural network, real-time processing.

For two-dimensional (2-D) FIR filter design, the conventional weighted least squares (WLS) technique rearranges the filter parameters of 2-D form into their corresponding one-dimensional (1-D) form, thus resulting in expensive computation. This paper presents a new computationally efficient WLS technique for the design of 2-D FIR filters. We introduce a updating desired frequency response which implicitly includes the weighting function such that the sum of weighted square errors to be minimized can be represented in a 2-D matrix form. This makes it possible to keep all filter parameters in their natural 2-D form, thereby reducing the computational complexity from O([N.sup.6]) to O([N.sup.3]). It is confirmed through design examples that the new technique is computationally very efficient and leads to nearly optimal approximations. This technique is suitable for the design of 2-D real zero-phase FIR filters with quadrantal symmetric or antisymmetric frequency response and can also be applied to the design of 1-D FIR filters. Index Terms - FIR filters, weighted least square.

Motion estimation plays an important role for the compression of video signals. This paper presents a new block-based motion estimation method using Kalman filtering. The new method utilizes the predicted motion and measured motion to obtain an optimal estimate of motion vector. The autoregressive models are employed to fit the motion correlation between neighboring blocks and then achieve predicted motion information. The measured motion information is obtained by the conventional block-based fast search schemes. Several algorithms based on either one- or two. dimensional models using either nonadaptive or adaptive Kalman filters are developed. The analysis of computational complexity and the simulation results indicate that the proposed method achieves significant savings on computation along with smoother motion vector fields and similar picture quality, when compared to the conventional full search algorithm.