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Laplace Transform

  1. Aug 15, 2013 #1
    Hi All,

    in a previous post on the physical meaning of Laplace's Transform I found the following statement
    " The fundamental Laplace transform pair is H(t), the Heaviside step function, and 1/s, its spectrum of damped sinusoids. Note that the spectrum is weighted towards low frequencies (1/abs(s) goes to zero as abs(s) goes to infinity), as one would expect for an excitation that begins but is never turned off".
    I am struggling to understand where the spectrum of damped sinusoids comes from, I found this interesting.
    Can anybody maybe help?
    Thanks a lot
     
  2. jcsd
  3. Aug 17, 2013 #2

    NascentOxygen

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    Staff: Mentor

    I interpret it thus:

    Bear in mind that to relate a Laplace transform back to the frequency (sinusoid wave) domain, we map s → jω.

    So 1/s → |1/ω| in magnitude, meaning amplitude of each component sinusoid is inversely proportional to its frequency.

    Beyond this, I can't say much more.
     
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