Ex 2.1 & 2.3 || Convolution || Discrete Time LTI System || End Ch Question 2.1(a) || (Oppenheim) 

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(English) || Example 2.1 & 2.3 || End Ch Question 2.1(a) || Discrete Time LTI System
Example 2.1: Consider an LTI system with impulse response h[n] and input x[n], as illustrated in Figure 2.3(a). For this case, since only x[O] and x[1] are nonzero, eq. (2.6) simplifies to the expression
y[n] = x[O]h[n- 0] + x[1]h[n - 1] = 0.5h[n] + 2h[n- 1]. (2.8)
Example 2.3: Consider an input x[n] and a unit impulse response h[n] given by
x[n] = anu[n],
h[n] = u[n],
Let
x[n] = 8[n] + 28[n- 1] - 8[n- 3] and h[n] = 28[n + 1] + 28[n- 1].
Compute and plot each of the following convolutions:
(a) YI [n] = x[n] * h[n] (b) Y2[n] = x[n + 2] * h[n]
(c) Y3 [n] = x[n] * h[n + 2]
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