Continuous-time and discrete-time signals :

A signal was defined as merely a mapping from one set to another. In certain cases, the independent variable is continuous, i.e. the elements of the domain set have a continuity associated with them. This means the mapping is defined over a continuum of values of the independent variable. Such signals are called continuous-time signals . A force pattern (force as a function of 2-dimensional space) or a speech signal would be an example of a continuous-time signal.

On the other hand, certain signals are defined for only discrete values of the independent variable; i.e. the elements of the domain are not continuous. Such signals are called discrete-time signals . India's population count, done every 10 years is an example of a discrete-time signal. In fact, the image files on your computer are also discrete-time signals; the information is stored pixel-wise, and not over a continuous stretch of 2 spatial co-ordinates. We typically index a discrete time variable by integers.

Note that it is not necessary that the co-domain of a discrete-time signal is discrete and that of a continuous-time signal is continuous.

Henceforth, we shall represent the independent variable for continuous-time signals by t (enclosed in (.) brackets), and for discrete-time signals by n (enclosed in [.] brackets).

As we are familiar with continuous-time signals, we shall now describe discrete-time signals in more detail.