Filter designs have number of applications in data transmission systems, perfect reconstruction filter banks, nonuniform sampling, interpolation filters over the past two decades. There are two conventional methods, which are FIR and IIR filter forms, to design filters. FIR filters can be designed with an exact linear phase. However, when the sharp magnitude specifications are required, higher order FIR filters are generally needed, and a larger delay results. On the other hand, IIR filters have two disadvantages: one is the stability that must be considered, and another is that the existing design methods are generally time consuming. For real-time signal applications, the above methods are all linear algebra based methods, therefore, cannot meet the requirements of real-time. Neural networks possessing parallel processing capability have been successfully applied for solving various computationally expensive optimization problems. This is due to the properties of guaranteed convergence to a local minimum of the Lyapunov energy function and the fast computational speed when implemented in hardware.