Fourier representation of CT peridic signals

AI Thread Summary
The discussion focuses on finding the Fourier coefficients for the signal cos²(2πt). The initial approach using the identity is nearly correct, as the correct expression is 1/2 + 1/2 cos(4πt). The complex definition can also be applied to derive the coefficients, leading to a_0 = 1/2 and a_1 = 3/4. Clarification was made regarding the notation, confirming that cos²(2πt) was intended. The conversation emphasizes the importance of accurate notation in Fourier analysis.
mbaron
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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
 
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\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.
 
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I meant the first, and thanks for the correction.
 
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