$x(t)= A+ A_1\sin (2 \pi f t + \theta ) + A_2\cos (2 \pi f_1 t + \theta )$ I want to find the Fourier transform $|\mathcal{F}[x(t)]|^2$ . Is this possible by hand? I can find the Fourier transform but then raise to power seems difficult.Is there any shortcut for this ?
Calculate by hand fourier transform of this sort of.
0
$\begingroup$
calculus
fourier-analysis
-
0@Pragabhava yes but the real part :) – 2012-10-03
1 Answers
1
Try using convolution rule (specific for this case): $\mathcal{F}[x(t)]\cdot\mathcal{F}[x(t)]=\frac{1}{2\pi}\mathcal{F}[x(t)\ast x(t)]$.