Fourier representation of CT peridic signals

[mbaron]

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

 

[AlephZero]

[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.

 

[mbaron]

I meant the first, and thanks for the correction.