Translations:Analog linear time-invariant systems/1/en

A continuous-time signal f(t) is a (real or complex) function that is defined for every real number t. The number t represents continuous time. A continuous-time signal also is called an analog signal. An important type of analog signal is the impulse function $\delta \left(t\right)$. This function plays the same role as does the discrete impulse function ${\delta }_{k}$, but it is not as easy to define. The impulse function $\delta \left(t\right)$, which also is known as the Dirac delta function, can be regarded as a generalized function. A generalized function cannot be defined as an isolated entity but instead must be viewed as the limit of a family of functions. Any family of functions ${\delta }_{\varepsilon }\left(t\right)$ with the following properties can be used to define the delta function $\delta \left(t\right)$. Here, $\varepsilon$ is a parameter that characterizes the functions ${\delta }_{\varepsilon }\left(t\right)$. The properties are