A model for echo generation is shown in Figure 10.20. (a) Calculate the transfer function H(z) =

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A model for echo generation is shown in Figure 10.20.

(a) Calculate the transfer function H(z) = Y(z)/X(z) of the echo sys-tem shown above.

(b) Suppose you would like to recover the original signal x[n] from  the output signal y[n] by passing it through a LTI system with  transfer function R(z). What should be R(z) so its corresponding  output is x[n]?

(c) Suppose that y[n] = u[n] ˆ’ u[n ˆ’ 2], find the original signal x[n].


Figure 10.20:

y[n] x[n] 0.5 0.25 ২

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