Designing a discrete time inverse system to eliminate distortion

Thread Starter

Mark Paul Dempsey

Joined Mar 29, 2016
I am trying to design a discrete-time inverse system to eliminate the distortion associated with 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 distorted received signal is expressed in terms of the transmitted signal as follows;
y[n] = x[n] + 0.9x[n-1]

I want to determine the unit impulse response of a causal inverse system that would discover x[n] from y[n], but I am at a loss as to how I should approach the problem.

My thinking is that I need to attach a system (h2[n]) in series with the system model of the communication channel h1[n], such that h2[n] is the inverse of h1[n]. To put it another way h1[n]*h2[n] = delta[n].

Can anyone offer some advice on the best way to go about this, or is there a procedure for such problems which I am as of yet unaware?