System Impulse Response

Once we learn about systems, both natural and man-made, we want to characterize them through a method. This is a standard scientific approach that is utilized in biology, physics, and space science. In physics, for example, we observe back-and-forth vibrations for a certain time when the strings of a guitar are plucked or when a tuning fork is struck on a surface. The term impulse response is not much different than this.

Response to an impulse

As the name implies, an impulse response is simply the output signal of a system when a unit impulse $\delta[n]$ is applied to its input. The impulse response of a system is denoted as $h[n]$.

For instance, an amplifier multiplies the input signal by a certain amount, say, by a factor of $10$. In the simplest terms, we can write its impulse response as:

$$\begin{equation*} h[n] = 10\delta[n] \end{equation*}$$

The impulse response of a discrete-time system $h[n]$ is in general a complex discrete-time signal, as shown in the figure below: