Echo generation of FIR system using Matlab
Generally, an echo of a signal is not just its delayed and weakened copy, but is characterized by an impulse response of the echo path. The basic model of an echo is a linear one.
In order to simulate a linear echo $E$ one will implement the following convolution:
$E = S * H, $
where $S$ is your sampled signal and $H$ is an echo path impulse response, both with the same sampling frequency.
The particular form of the impulse response $H$ depends on the echo path. For example, $H$ may include $N$ zero values at the beginning to simulate an echo delay $N$.
Note, that in case of an acoustic echo, the linear impulse response $H$ may be not enough since an echo path is usually non-linear.