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Suppose there exists a sequence $x(n)$ Then let \[y(n) = 0.9 x(n) + 0.8x(n - 1) - 0.5y(n - 1)\] Test Of Linearity Let \[x(n) = a x_1(n) + b x_2(n)\] Substitute \[y(n) = 0.9(a x_1(n) + b x_2(n)) + 0.8(a x_1(n - 1) + b x_2(n - 1)) - 0.5 y(n - 1)\] \[y(n) = a(0.9 x_1(n) + 0.8 x_1(n - 1)) + b(0.9 x_2(n) + 0.8 x_1(n - 2)) - 0.5 y(n - 1)\]
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Fri, 27 Oct 2017 12:19 GMT