laplace transform thingies

Discussion in 'Homework Help' started by S_lannan, Apr 5, 2008.

  1. S_lannan

    Thread Starter Active Member

    Jun 20, 2007
    247
    2
    any basic texts on what the hell they are / do / are used for in EE??

    i'm going to uni next year and would like to get a head start on a few university topics studied in electronics engineering.

    cheers
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Try here at Wikipedia.

    hgmjr
     
  3. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    And here also.

    hgmjr
     
  4. S_lannan

    Thread Starter Active Member

    Jun 20, 2007
    247
    2
    well.

    looks like i got a bit of work ahead of me, the mathematics used are completely alien to me.
     
  5. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Laplace Transforms are widely used in control systems analysis and analysing analog circuits (some of the analog experts here will tell you how prevalent the techniques are from a practical perspective - I'm not sure).

    The fundamental bilateral equation is: http://upload.wikimedia.org/math/b/d/b/bdb9d6ca4bbf485387d7a13749c9863a.png - All Laplacian identities are derived from this equation.

    For any time-based function f(t) you can (attempt!) to derive the Laplacian representation of the equation. What the Laplace transform does is maps the time-domain function f(t) to the s-plane, where the functions are frequency-based. If you have done Fourier analysis then Laplace transforms are almost identical however where the s-parameter is a complex number with real and imaginary part, in Fourier analysis s is completely imaginary.
     
  6. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    You will cover Laplace Transforms as part of a Signal and Systems course. The mathematical constucts should be taught in 2nd semester maths, but if you are curious look at "Signals and Systems" by Oppenheim (and some other bloke, I can't remember his name).

    Sedra and Smith will show you how Laplace Transforms are used in understanding practical electronic circuits.

    Dave
     
  7. colsandurz

    New Member

    Apr 7, 2008
    2
    0
    Try
    Oppenheim & Wilsky
    or
    B.P. Lathi
    I can't remember the titles, but they're both pretty generic titles. As far as the contents are concerned they're both very similar, they're just organized differently(ie one separates discrete and continuous time and the other doesn't). Also, learn differential equations first, because you won't understand any the material in these books if you don't know any differential equations.
     
  8. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Yes, Wilsky is the other author who writes "Signals and Systems". Couldn't remember his name. Thanks.

    Dave
     
  9. S_lannan

    Thread Starter Active Member

    Jun 20, 2007
    247
    2
    ok cheers guys.

    first off my calculus is in great need of revision... that will be the first stop :)
     
  10. scubasteve_911

    Senior Member

    Dec 27, 2007
    1,202
    1
    Basically, the laplace transform helps you solve differential equations! It turns a difficult calculus question into a more of an algebraic equation via the transform.

    You'll definitely learn the algebra tricks that you need to apply to inverse the transform, such as partial fraction expansion, completing squares, factoring so that you can use existing laplace transform pairs, etc.

    Steve
     
  11. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    How could we have missed that one!

    \frac{dy}{dx}\rightarrowsY(s)

    \frac{d^{2}y}{dx^{2}}\rightarrows^{2}Y(s)

    And so on...

    Dave
     
  12. scubasteve_911

    Senior Member

    Dec 27, 2007
    1,202
    1
    hehe, It is a lot better than trying to do friggin silly 'sturm louisville' based solutions :p
    Hands down to Laplace for making my life so much easier :D

    Steve
     
  13. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
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    Not just a bit easier, but much easier - multi-order differential equations to multiplication and division - very nice :D

    Mind you, we'd just bang it into Matlab or Octave these days!

    Dave
     
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