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Fourier notation

  1. May 12, 2014 #1
    The Fourier integrals and series can be written of 3 forms (possibly of 4):

    the "real cartesian":
    a(ω)cos(ωt) + b(ω)sin(ωt)

    the "real polar":
    A(ω)cos(ωt - φ(ω))

    where:
    A² = a² + b²
    sin(φ) = b/A
    cos(φ) = a/A
    tan(φ) = b/a

    the "complex polar"
    A(ω)exp(iφ(ω))exp(iωt)

    And my doubts are: 1) exist a "complex cartesian" correspondent? 2) is possible to connect the real forms with the complex forms?
     
  2. jcsd
  3. May 12, 2014 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The Euler identity is the connection.
    exp(ix) = cos(x) + isin(x)
     
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