Question: Consider designing a DT inverse system to eliminate the distortion associated with an undesired echo in a data transmission problem. Assume the echo is

Consider designing a DT inverse system to eliminate the distortion associated with an undesired echo in a

Consider designing a DT inverse system to eliminate the distortion associated with an undesired echo in a data transmission problem. Assume the echo is represented as attenuation by a constant factor a and a delay corresponding to 1 time unit of the input. Hence the distorted received signal is: y[n] = x[n] + ax[n 1] Note here, that the impulse response is: h[n] = 1, n = 0 a, n = 1 (0, otherwise The inverse of this impulse response must satisfy: h[n] * h [n] = 8[n] Substituting for h[n], we desire to find h- [n] that satisfies the equation h [n] +ah [n - 1] = 8[n]. Find a causal inverse system, h[n] in order to recover x[n] from y[n].

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