Abstract:
This thesis addresses the use of dynamic neural networks in the spectral estimation problem. The first phase of our contribution is used to estimate the line spectrum of a signal modeled by the sum of a set of complex sinusoids whose frequencies are known using the complex-valued Hopfield neural network. This approach has been generalized to estimate the three parameters of the model signal simultaneously; frequency, amplitude and phase from the available samples and without any a prior information on the signal using a modified Hopfield network. This phase was followed by the use of a dynamic neural network proposed for estimating the autoregressive spectral density. Then the last network has been introduced into the non-parametric method of minimum variance. This approach consists in calculating the AR coefficients by the Zhang neural network in solving the Yule Walker equations, and then uses the Marple et al. algorithm to assess the power spectral density. Following the Toeplitz structure of the system to be solved, a reduced architecture of the Zhang neural network has also been proposed. Our contribution was completed by using the Zhang network to reverse the correlation matrix to estimate the amplitude of a multidimensional signal spectrum. Simulation results show the superiority of the proposed approaches for the speed and the ease of implementation compared to the conventional methods which qualify these technics for real-time applications
