I am trying to design a discrete-time inverse system to eliminate an undesired echo in a data transmission problem.
The echo caused by the transmission channel is represented as attenuation by a factor of 0.9 and a delay corresponding to one time unit of the input sequence.
The received signal $y[n]$ can be expressed as follow;
$$y[n] = x[n] + 0.9x[n-1]$$
So basically, I'm trying to determine the unit impulse response of a causal inverse system to discover $x[n]$ from $y[n]$.
Conceptually, I'm thinking I need to connect a system $h_2[n]$ in series with the system $h_1[n]$ such that $h_1[n]*h_2[n] = \delta[n]$.
Can anyone offer some advice on how best to go about this ? I've been searching online but can't find a concrete example to use as a starting point.