Fourier representation of CT peridic signals

[mbaron]

I want to find the Fourier coefficients for the following signal:

\cos(2 \pi t)^2

Can I simply use the identity?:

\frac{1}{2} + \frac{\cos(2 \pi t)}{2}

And then use the complex definition:

\frac{1}{2} + \frac{1}{4} (\exp{j2 \pi t} + \exp{-j2 \pi t})From the synthesis equation I can get:
a_0 = \frac{1}{2}, a_1 = \frac{3}{4}

Thanks

 

[AlephZero]

\cos(2 \pi t)^2 is a strange (non-standard) notation.

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


If you mean \cos(4 \pi^2 t^2) then it is not.

 

[mbaron]

I meant the first, and thanks for the correction.