This thesis is concerned with the problem of signals and systems identification applied to digital communication. Whilethe majority of the existing methods are stochastic, we propose an algebraic and deterministic approach. Moreover, wewill treat signals and systems directly in continuous time, which enables us to explore the knowledge of their shape,that may be hidden or forgotten by the sampling operation. Furthermore, the proposed techniques are simple and rapid,what allows their on-line implementation.Firstly, we consider the problem of correcting distortions in a power-line communication system, exploring its flatnessproperty. The inverse system obtained is then applied to another context, more specifically to the restoration of thevoice timbre in telephone networks.Afterwards, the system identification problem is considered in the context of a new deterministic theory, based ondifferential algebra and operational calculus. This theory gives rise to a new general algorithm for the input-outputidentification of a rational system. The rapidness of estimation also allows the presentation of the local filteringnotion, which consists in representing a high dimension system by a time-varying low dimension model. This approach isinteresting since it permits the direct demodulation of the received signal, without the need of explicitly identifyingor equalizing the channel.Finally, the demodulation of a continuous phase modulation signal is addressed in the light of the algebraic techniquesproposed. The solution consists in describing the received signal, at each symbol period, as a linear differentialequation (generally with time-varying coefficients), with coefficients that are functions of the current symbol.Therefore, the symbol by symbol demodulation becomes immediate and particularly robust to noise.
