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?
Thanks
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?
Thanks
