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Question Number 202771 by ali009 last updated on 03/Jan/24

d e t e r m i n e w h e t h e r t h i s s i g n a l i s p e r i o d i c

o r n o t i f {i t}^{'} s p e r i o d i c s p e c i f y {i t}^{'} s

f a u n d e m w n t a l p e r i o d

y (n) = c o s (\frac{n}{8}) c o s (\frac{n π}{8})

Answered by Frix last updated on 03/Jan/24

{It}^{'} s not periodic . To see what happens :

π \approx 3

\cos \frac{n}{8} \cos \frac{3 n}{8} \Rightarrow period is 8 π

π \approx \frac{22}{7}

\cos \frac{n}{8} \cos \frac{11 n}{28} \Rightarrow period is 112 π

π \approx \frac{355}{113}

\cos \frac{n}{8} \cos \frac{355 n}{904} \Rightarrow period is 904 π

\dots

\cos \frac{n}{8} \cos \frac{n π}{8} \Rightarrow period is \infty

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