Fourier Series

Discussion in 'Math' started by RdAdr, Oct 18, 2015.

  1. RdAdr

    Thread Starter Member

    May 19, 2013
    214
    1
    Consider the following article:
    https://en.wikipedia.org/wiki/Fourier_series

    At definition, they say that an = An*sin() and bn = An*cos()

    So with these notations you can go from a sum having sin and cos to a sum having only sin but with initial phases.

    Why can I write an = An*sin() and bn = An*cos() ?
    It seems out of the blue.
     
  2. RdAdr

    Thread Starter Member

    May 19, 2013
    214
    1
    I figured it out. It follows from Pythagora's theorem in a right angle triangle.
     
  3. Motanache

    Member

    Mar 2, 2015
    70
    4
    It is not that difficult.
    Look at this figure:
    [​IMG]

    In the first image we have square signal.

    But a radio device receives a sine wave.
    LC oscillate as Sin():
    https://en.wikipedia.org/wiki/RLC_circuit

    So in the first image signal approaches with Sin() drew orange.
     
    Last edited: Oct 18, 2015
  4. Motanache

    Member

    Mar 2, 2015
    70
    4
    It is the main component of which will receive a radio, if you give a rectangular signal as in the first image.

    In fact, RLC react to a growth rate (di/dt):
    [​IMG]

    And the margins are 'very steep', that means I had very high frequency component.
    So, what I could add up to that SIN ()(orange line) to drown the steep edges? corners.

    This is the case sinusoids of blue and green.

    Because we can not hatching the entire rectangle so, something must also substracted. Therefore we have cosine.
     
    Last edited: Oct 18, 2015
  5. Motanache

    Member

    Mar 2, 2015
    70
    4
    Forming a rectangular signal from sine signal:
    [​IMG]
    [​IMG]
     
  6. RdAdr

    Thread Starter Member

    May 19, 2013
    214
    1
    Thanks for the answers.
     
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