# Representations of the Fourier's integral

1. Jan 27, 2014

### Jhenrique

If exist 3 representations for fourier series (sine/cosine, exponential and amplite/phase) and at least two fourier integral that I know
$$f(t)=\int_{0}^{\infty }A(\omega)cos(\omega t) + B(\omega)sin(\omega t)d\omega$$
$$f(t)=\int_{-\infty }^{+\infty }\frac{e^{+i\omega t}}{\sqrt{2\pi}} F(\omega)d\omega$$
So, exist too a representation for fourier integral in amplitude/phase notation? How is it?
Other question: $A(\omega)$ and $B(\omega)$ are the sine and cosine transforms?
And another ask: I can relates F(ω) with A(ω) and B(ω), like we do in series fourier $\left (|c_{n}|=\frac{1}{2}\sqrt{a_{n}^{2} + b_{n}^{2}} \right )$?