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.