Drill 7.10 (Using the Convolution Property) Using the (time-domain) convolution property of Eq. (7.26) and appropriate pairs in Table 7.1, show that u[n]u[n 1] = nu[n].

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▷ Drill 7.10 (Using the Convolution Property)
Using the (time-domain) convolution property of Eq. (7.26) and appropriate pairs in Table 7.1, show that
u[n]u[n 1] = nu[n].
Drill 7.10 (Using the Convolution Property)
From Table 7.1, we know that
u[n] 1 and u[n − 1] 2 ³
Using the convolution property, we find that
( ه -
=
u[n] * u[n − 1] ←² (⁄²-₁) (= -₁).
both with |z|>1.
|2| > 1.
Using pair 5 of Table 7.1 with y = 1, we see that the z-transform (1) also corresponds to the
signal nu[n]. Thus,
u[n]u[n 1] = nu[n].
Transcribed Image Text:▷ Drill 7.10 (Using the Convolution Property) Using the (time-domain) convolution property of Eq. (7.26) and appropriate pairs in Table 7.1, show that u[n]u[n 1] = nu[n]. Drill 7.10 (Using the Convolution Property) From Table 7.1, we know that u[n] 1 and u[n − 1] 2 ³ Using the convolution property, we find that ( ه - = u[n] * u[n − 1] ←² (⁄²-₁) (= -₁). both with |z|>1. |2| > 1. Using pair 5 of Table 7.1 with y = 1, we see that the z-transform (1) also corresponds to the signal nu[n]. Thus, u[n]u[n 1] = nu[n].
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