Design of arbitrary-delay M-band cosine-modulated wavelet based on neural network

In order to obtain the M-band wavelet with better frenquency selectivity, an optimum desigh method for arbitrary-delay M-band cosine-modulated wavelet was proposed. Based on the perfect reconstruction filter theory, different M-band biorthogonal and orthogonal wavelets can be designed through revising the system delay parameters. When the parameter design was performed for the simplified secondary objective function and constraint condition, an augmented Lagrangian multiplier method was used to convert the problem into an unconstrained optimization problem in an equivalent way. And an optimum design structure based on discrete time Hopfield neural network was proposed. The iterative operation was performed with steepest descent method to reduce the complexity of the algorithm. Compared with the existing algorithms, the proposed method has such advantages as simple realization, high efficiency and better optimum performance.