A signal can be defined as an abstraction of any quantity that can be measured, which is function of at least one independent variable (time or space). A signal is the functional representation of a physical quantity or variable, and it contains information about the behavior of the physical quantity.

Example of signals:

**electrical**: voltage and current**mechanical**: position and speed**hydraulic**: pressure and flow

The **sound** coming to our ears is also a signal. A **picture** within a book, a **movie** on the TV screen, they are also signals.

Mathematically, a signal is represented as a function of an independent variable *t*. Most of the time t stand for **time**. The mathematical notation of a signal is *x(t)*.

Depending on the continuity of the contained information signals can be:

**continuous-time****discrete-time**

A **continuous-time signal** has a value for all instants in time or space. Example of a continuous-time signal is the voltage of a battery or the position of a pendulum.

A **discrete-time signal** has a value only at discrete moments in time. Example of a discrete signal is the weight of a human measured early or the daily average temperature measure in a specific area.

Very often, discrete-time signals are **sampled** versions of continuous time signal. For example, if we measure the voltage of a battery at a specified time interval (e.g. every second) we’ll end up with a discrete-time signal.

If *x(t)* is a continuous-time signal, and we sample it at *t _{0}, t_{1}, … t_{n}*, we get

**samples**:

In a shorter form we can write the samples as:

\[x[0], x[1], … , x[n]\]or even shorter:

\[x_0, x_1, … , x_n\]Generally speaking:

\[ \begin{equation} \begin{split}\bbox[#FFFF9D]{x_n=x[n]=x(t_n)}

\end{split} \end{equation} \]

The time interval between two adjacent samples is called **sampling interval**. When the sampling interval is constant for the whole measurement, we’ll have an **uniform sampling**, which means:

where *T _{s}* is the sampling interval.

A **continuous-time signal** can be defined with the help of **mathematical function**. For example:

t &= – 2 \pi … 2 \pi\\

x(t) &= sin^2(t)+cos(t)\\

\end{split} \end{equation*} \]

The graphical representation of this signal is:

A **discrete-time signal** can be defined in several ways:

- as a
**function**:

- as a
**table**:

n | … | -3 | -2 | -1 | 0 | 1 | 2 | 3 | … |

x[n] | … | 0 | 2 | 1 | 0 | 1 | 2 | 0 | … |

- as a
**sequence of values**:

- as a
**vector**:

- as
**graphical representation**

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## herve Bernad

Merci pour votre def de ce qu’est un signal !