In this Thesis contributions are made to signal processing and system simulation using digital techniques and microprocessor based systems. The aim was to find methods and design fast digital systems for real-time applications, and to develop signal processing and system simulation algorithms implemented in microprocessor-based systems. Starting with the discussion of the available approximation methods for the computation of the binary logarithm, a new method together with its digital hardware implementation is given. The analysis and synthesis of analogue signals with hardware methods using Walsh functions are examined, and their implementation with integrated circuits is given. A data-compression method based on the fast Walsh transform (FWT) is given and a new implementation using a multi-microcomputer system is proposed. The method is applied to the compression of electrocardiogram signals. A piece-wise linear approximation algorithm suitable for real time applications is proposed, and its implementation in a microcomputer based system for data reduction of an electrocardiogram signal, is given. An extension of this algorithm for the QRS complex detection, is presented. Finally, some basic matrix operation-algorithms suitable for system analysis and synthesis are examined and implemented using a microprocessor-based system. The computation of the response (simulation) of a given system applying the above algorithms is carried out on a microcomputer development system. Most of the techniques considered and developed in this Thesis were practically implemented and tested either with real or with simulated data.