14. Consider the first-order system described by the difference equation y[r] – {y[n – 1) = r[n]. (a) Find the total solution for n > 0 when the input signal is x[n] = 2u[n] given the initial condition y[–1] = 3, the complementary solution Ye[r] = a1(})" where a is a constant to be determined, and the particular solution Yp[n] = (3 – (})"), n>0. %3D (b) Without using transforms, obtain an expression for the impulse response of the system.

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14. Consider the first-order system described by the difference equation
y[r] – {y[n – 1) = r[n].
(a) Find the total solution for n > 0 when the input signal is x[n] = 2u[n] given the
initial condition y[–1] = 3, the complementary solution
Ye[r] = a1(})"
where a is a constant to be determined, and the particular solution
Yp[n] = (3 – (})"), n>0.
%3D
(b) Without using transforms, obtain an expression for the impulse response of the
system.
Transcribed Image Text:14. Consider the first-order system described by the difference equation y[r] – {y[n – 1) = r[n]. (a) Find the total solution for n > 0 when the input signal is x[n] = 2u[n] given the initial condition y[–1] = 3, the complementary solution Ye[r] = a1(})" where a is a constant to be determined, and the particular solution Yp[n] = (3 – (})"), n>0. %3D (b) Without using transforms, obtain an expression for the impulse response of the system.
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