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

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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 ¹ [n] = 8[n] Substituting for h[n], we desire to find h-¹ [n] that satisfies the equation h¹ [n] +ah ¹ [n - 1] = 8[n]. Find a causal inverse system, h¯¹[n] in order to recover x[n] from y[n]. 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 ¹ [n] = 8[n] Substituting for h[n], we desire to find h-¹ [n] that satisfies the equation h¹ [n] +ah ¹ [n - 1] = 8[n]. Find a causal inverse system, h¯¹[n] in order to recover x[n] from y[n].

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In this problem we are trying to find an inverse system h1n that can recover the original signal xn ... View the full answer