Two filters are defined as follows: Filter 1 has input signal (n) and output signal...

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Two filters are defined as follows: • Filter 1 has input signal æ(n) and output signal y1 (n) and has transfer function H(2) = 1+2z!. • Fiter 2 has the same input signal r(n) with output signal y2(n). The difference equation for this filter is 42(n) æ(n) + 1.892(n – 1) – 0.9y2(n – 2). %3D The input is a zero-mean white signal with a variance of 2. a) Calculate the variance, of, of y1(n). b) Calculate the variance, o, of y2(n). c) Filter 2 is replaced by a filter with transfer function -1 H2(2) %3D 1- 0.92 The outputs of the two filters are then added as follows to give an overall output y(n). y(n) Vı(n) + 2(n) %3D Calculate the variance, a?, of y(n). Two filters are defined as follows: • Filter 1 has input signal æ(n) and output signal y1 (n) and has transfer function H(2) = 1+2z!. • Fiter 2 has the same input signal r(n) with output signal y2(n). The difference equation for this filter is 42(n) æ(n) + 1.892(n – 1) – 0.9y2(n – 2). %3D The input is a zero-mean white signal with a variance of 2. a) Calculate the variance, of, of y1(n). b) Calculate the variance, o, of y2(n). c) Filter 2 is replaced by a filter with transfer function -1 H2(2) %3D 1- 0.92 The outputs of the two filters are then added as follows to give an overall output y(n). y(n) Vı(n) + 2(n) %3D Calculate the variance, a?, of y(n).