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Fourier representation of CT peridic signals

  • Thread starter mbaron
  • Start date
  • #1
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I want to find the Fourier coefficients for the following signal:

[tex] \cos(2 \pi t)^2 [/tex]

Can I simply use the identity?:

[tex] \frac{1}{2} + \frac{\cos(2 \pi t)}{2} [/tex]

And then use the complex definition:

[tex] \frac{1}{2} + \frac{1}{4} (\exp{j2 \pi t} + \exp{-j2 \pi t}) [/tex]


From the synthesis equation I can get:
[tex] a_0 = \frac{1}{2} [/tex], [tex] a_1 = \frac{3}{4} [/tex]

Thanks
 
Last edited:

Answers and Replies

  • #2
AlephZero
Science Advisor
Homework Helper
6,994
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[tex] \cos(2 \pi t)^2 [/tex] is a strange (non-standard) notation.

If you mean [tex] \cos^2(2 \pi t)[/tex] then your method is almost correct - it equals [tex] \frac{1}{2} + \frac{\cos(4 \pi t)}{2} [/tex]


If you mean [tex] \cos(4 \pi^2 t^2)[/tex] then it is not.
 
Last edited:
  • #3
6
0
I meant the first, and thanks for the correction.
 

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