CDS 212 - Solutions to Homework # 2
نویسنده
چکیده
(a) [Problem 2.2 in DFT] For u 1 : For u 2 : For u 3 : Note that u 1 = u 2 2 = ∞ 0 1 · dt = ∞, while u ∞ = 1 and P ow(u) = lim T →∞ 1 2T T 0 1 · dt = 1 2. T −T u 2 (t)dt = T 0 u 2 (t)dt = T 0 |u(t)|dt = k−1 i=0 2 2i for 2 2k−1 ≤ T ≤ 2 2k , k ≥ 1. Hence, u 1 = u 2 = ∞ while u ∞ = 1. Finally: P ow(u) = lim T →∞ 1 2T T −T u 2 (t)dt = lim k→∞ 1 2 2k k−1 i=0 2 2i = 1 4 when T = 2 2k−1 , k ≥ 1 lim k→∞ 1 2 2k+1 k−1 i=0 2 2i = 1 8 when T = 2 2k , k ≥ 1 Hence the limit is not well-defined and u is not a power signal.
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