A continuous signal or a continuous time signal is a varying quantity (a signal) that can be, or is expressed, as a continuous function of an independent variable, usually time.

The signal is defined over a duration, which may or may not be finite, and there is a one to one mapping of the value of the signal from the time. This basically means at any given time the signal is uniquely defined. The continuity of the time variable, in connection with the law of density of real numbers, means that the signal value can be found at any arbitrary location, t₀. Please refer to Real vs. ...

A typical example of an infinite duration signal is:

f(t) = sin (t); -infinity ≤ t ≤ infinity

A finite duration counterpart of the above signal could be:

f(t) = sin (t); -pi ≤ t ≤ pi

f(t) = 0; otherwise

There are several schools of thoughts the values that the range of the function should include. One school of thought is a finite (or infinite) duration signal may or may not be finite valued. For example,

f(t) = 1/t; 0 ≤ t ≤ 1

f(t) = 0; otherwise

is a finite duration signal but it takes an infinite value for t = 0.

However, the second and possibly more prevalent school of thought is that infinity is not a limit and hence, a continuous signal must always have a finite value. This, of course, makes more sense in the case of real life continuous signals, which cannot take up infinite values in any case.

Any analogue signal is continuous by nature. Discrete signal, used in digital signal processing, can be obtained by sampling of continuous signals using a sampling function (usually a train of time-shifted impulses of the dirac delta function). A discrete signal is a signal that has been sampled from a continuous signal. ... Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. ... In general, a sample is a part of the total, such as one individual or a set of individuals from a population (of people or things), a small piece or amount of something larger, a number of function values of a function, or part of a song. ... The Dirac delta function, sometimes referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere such that the total integral...

Continuous signal may also be defined over an independent variable other than time. Another very common independent variable is space and is particularly useful in image processing. Image processing is the application of signal processing techniques to the domain of images — two-dimensional signals such as photographs or video. ...