A constrained neural network with complex activation function: application to time-frequency analysis

Many signal processing problems need to be solved in an adaptive way under some constraints. The paper introduces a constrained complex-valued neural network (CCNN) model. It is composed of two sub networks: a master which gives the main energy function (the error power between the master´s output and a desired output), and a slave which gives a secondary energy function (related to the constraints imposed by the problem). The sum of these energy functions gives the cost function to be minimized by the CCNN. An extension of the classical back propagation algorithm to the complex plane, under some inequality constraints, is used for the training process. This model finds a natural application in the time-frequency analysis as it gives direct access to the time-frequency signature