# impulse response

Impulse response is the reaction of the system to a series of instantaneous pulses.

In the context of channel taps, the impulse response, \(h\) is given by

\begin{equation}
h(t, \tau) = \sum_{i = 1}^{N} c_i(t)\delta(\tau - \tau_i)
\end{equation}

Where \(N\) is the number of taps, \(c_i\) is the channel, and \(\delta\) is the kronecker delta function.

Also note that the "channel" here refers to the physical channel, in between the transmitter and receiver's modifications.

This should be interpreted as the linear convolution between the channel and the delta impulse function.

For a linear time invariant system, this is all that is necessary to fully define the channel.