Digital Signal Filtering, Analysis and Restoration

Signal processing is an important and fast developing area with applications in very different regions of human activity from traditional communications and multimedia technology through measurement evaluation and system identification in mechanical, civil, electrical or chemical engineering, in physical as well as human sciences, in medicine and biomedical applications, ecological and economic analyses and futurology. The traditional concept of signals as continuous functions of time (so-called analogue signals) has gradually widened to include signals formed by discrete series and even multidimensional discrete signals. These discrete signals may, although not necessarily, originate from continuous-time (or continuous-space) signals by means of sampling. As proven in signal theory, the original continuous signal can be perfectly recovered from samples under certain conditions, and therefore the information value of the discrete form is equivalent to that of the continuous function. It follows that all the results achievable by classical continuous-time methods can in principle also be obtained by discrete processing. However, discrete methods offer much more: complex and demanding methods can be realised that would be unreliable or even not actually feasible in the continuous version (e.g. adaptive and learning methods); signals, the continuous versions of which do not exist (e.g. sequences of economic data), can be effectively processed and analysed. Also, if the discrete values are expressed as numbers, the signal processing system can cooperate directly with digital information systems which provide time-unlimited mass memory in data archives. These features have led to the gradual replacement of analogue signal processing methods by discrete...