An LTI system represented by the difference equation y[n] = y[n 1] + x[n], n ¥ 0, is initially at rest. The input of the system is x[n] and the output y[n]. (a) Using the difference equation find the system response y[n] for n ¥ 0 when the input is Find y[n] for n = 1, 0, 1 ¦ ,10 (b) Using the above result and the linearity and time-invariance of the system find the output y 1 [n] corresponding to a new input 0, 1, 2 %3 x[n] otherwise n = 0, 1, 2, 3, 4, 5 x[n] = otherwise

Question: An LTI system represented by the difference equation y[n] = y[n 1] + x[n], n ¥ 0, is initially at rest. The input of the

An LTI system represented by the difference equation y[n] = ˆ’ y[n ˆ’ 1] + x[n], n ‰¥ 0, is initially at rest. The input of the system is x[n] and the output y[n].

(a) Using the difference equation find the system response y[n] for n ‰¥ 0 when the input is

0, 1, 2 п %3 x[n] otherwise

Find y[n] for n = ˆ’1, 0, 1 €¦ ,10

(b) Using the above result and the linearity and time-invariance of the system find the output y₁[n] corresponding to a new input

n = 0, 1, 2, 3, 4, 5 x[n] = otherwise

0, 1, 2 п %3 x[n] otherwise n = 0, 1, 2, 3, 4, 5 x[n] = otherwise

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