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 h¹ [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 h¹ [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
Related Book For
Discrete Time Signal Processing
ISBN: 9780137549207
2nd Edition
Authors: Alan V. Oppenheim, Rolan W. Schafer
Posted Date:
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