[作業] 信號HW1 #1
我是這樣寫的：
(a) x(t+T) = {cos[2pi(t+T)]}^2
= (cos 2pi*t * cos 2pi*T - sin 2pi*t * sin 2pi*T)^2 ≠ x(t)
→ Not periodic.
(b) x[n+N] = (-1)^(n+N)^2 = (-1)^n^2 + (-1)^(2nN + N^2) ≠ x[n]
→ Not periodic.
(c) x[n+N] = cos[4(n+N)] = cos 4n * cos 4N - sin 4n * sin 4N ≠ x[n]
→ Not periodic.
可是3個都非週期性太不自然了@@
我應該有某些地方弄錯了
請大家指點迷津 感謝
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◆ From: 61.31.169.93
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剛算了一下 發現(a)用半角還是會有cos[4pi(t+T)] 用和角拆開後就回到原文了
隨便取個sin4pi*T來看 因為T可以是任意實數 所以sin4pi*T = [-1, 1] 其他三項同理
所以我覺得是非週期性
另外(b) (-1)^(n^2)*(-1)^(2nN + N^2) = (-1)^(n^2) * 1 * (-1)^(N^2)
(-1)^(N^2)要看N是奇數或偶數才能決定是-1或+1 所以我覺得是非週期性
以上不知道有沒有錯@@
麻煩大家指正 感謝
※ 編輯: alanalg 來自: 61.31.169.93 (03/13 11:56)
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