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Representations of the Fourier's integral

  1. Jan 27, 2014 #1
    If exist 3 representations for fourier series (sine/cosine, exponential and amplite/phase) and at least two fourier integral that I know
    [tex]f(t)=\int_{0}^{\infty }A(\omega)cos(\omega t) + B(\omega)sin(\omega t)d\omega[/tex]
    [tex]f(t)=\int_{-\infty }^{+\infty }\frac{e^{+i\omega t}}{\sqrt{2\pi}} F(\omega)d\omega[/tex]
    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 )##?
  2. jcsd
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