Signal classification

With reference to the scheme of a direct digital control system (DDC) it can be observed that it is composed, in most cases, of one part (actuator, process and transducer) continuous-time, while the regulator is discrete-time. In addition, there are signals of various types, digital inside the regulator and analog outside: the task of the interface is to provide for the conversion of the signals. It is, therefore, necessary to characterize in a mathematical way these signal conversions that are, on the other hand, well known in the field of Signal Theory and Electrical Communications.

Classification of signals over time

Deterministic signal: it is represented by a real function of a real variable in which the independent variable is the time that we will indicate with t.

Time-continuous signals: the independent variable t (time) assumes all the values of a continuous set, such as the entire real axis. The formal expression is s=s(t).

Time-discrete signals: the variable t takes values in a countable set {t_k} where k is an integer. They are represented with s=s(t_k) or as a {s_k} timeline. In most applications, the instants t_k are a fixed interval T away from each other, in which case the notation s=s(kT) or s=s(k) is also used.

Classification of signals in amplitude

Continuous signals in amplitude: the dependent variable assumes all the values in a continuous set.

Discrete signals in amplitude (or quantized): the dependent variable assumes values in a countable set that, in most cases, is finite.

Deterministic signals can then be classified into:

• Analog signals: continuous signals over time and amplitude. For example the controlled output of the DDC chain, the output of a potentiometer, etc.
• Quantized signals: time-continuous and discrete signals in amplitude, such as, for example, the actuator control signals that are obtained from the digital-analog conversion of the numerical data processed by the algorithm.
• Digital (or numeric) signals: discrete signals both in time and amplitude, such as, for example, the data processed by the control algorithm of a DDC ring.
• Discrete signals: discrete signals over time and continuous in amplitude. An example of a discrete signal is the instantaneous frequency of a train of pulses that are generated at times t_k, and defined by: