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Thread: Difference equation - algebra

  1. #1
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    Difference equation - algebra

    Hello,

    how can I get:

    $\displaystyle y[k](\frac{T}{T_v}+1) = Kx[k] + \frac{T}{T_v}y[k-1]$

    to this:

    $\displaystyle y[k]= \frac{T_v K}{T+T_v}x[k] + \frac{T}{T_v + T}y[k-1]$

    ? I would need detail derivation.

    Thanks.
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  2. #2
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    Re: Difference equation - algebra

    seriously?

    just divide both sides by $\dfrac{T}{T_v} + 1$
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  3. #3
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    Re: Difference equation - algebra

    Yes, seriously

    So this is equal if I multiply with:

    $\dfrac{T_v}{T} + 1$
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  4. #4
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    Re: Difference equation - algebra

    I can believe you are serious. You seriously need to learn algebra! "Dividing by $\displaystyle \frac{T}{T_v}+ 1$" is not "multiplying by $\displaystyle \frac{T_v}{T}+ 1$"! $\displaystyle \frac{T_v}{T}+ 1= \frac{T_v}{T}+ \frac{T}{T}= \frac{T_v+ T}{T}$. Dividing by that is the same as multiplying by $\displaystyle \frac{T}{T_v+ T}$.
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  5. #5
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    Re: Difference equation - algebra

    Quote Originally Posted by Nforce View Post
    Yes, seriously

    So this is equal if I multiply with:

    $\dfrac{T_v}{T} + 1$
    no ....

    $\dfrac{1}{\dfrac{T_v}{T}+1} = $

    $\dfrac{1}{\dfrac{T_v+T}{T}} = $

    $\dfrac{T}{T_v + T}$
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  6. #6
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    Re: Difference equation - algebra

    Quote Originally Posted by romsek View Post
    no ....
    Romsek, wear a hockey helmet !
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  7. #7
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    Re: Difference equation - algebra

    Thanks, sorry if I am an idiot but I don't use math in my daily life.

    I have other one which is a bit difficult:

    How do we get this:
    $\displaystyle y[k] = K x[k] + K \sum_{i=0}^{k-1}x[i]$

    to:

    $\displaystyle Kx[k] + y[k-1]$

    This last one is a recursive equation.
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  8. #8
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    Re: Difference equation - algebra

    Quote Originally Posted by Nforce View Post
    Thanks, sorry if I am an idiot but I don't use math in my daily life.

    I have other one which is a bit difficult:

    How do we get this:
    $\displaystyle y[k] = K x[k] + K \sum_{i=0}^{k-1}x[i]$

    to:

    $\displaystyle Kx[k] + y[k-1]$

    This last one is a recursive equation.
    This last one isn't an equation at all! Are you trying to solve for Kx[k] + y[k - 1]? If then just write out what y[k - 1] will be and then you can write out an expression for x[k] and y[k - 1]. This isn't the hard part. The hard part is to try to simplify the answer (I'm assuming you need to do that) and for that you'll have to find a way to handle the summation.

    Hint: The summation just adds up a series of terms x[0] + x[1] + ... + x[k - 1].

    -Dan
    Last edited by topsquark; Jan 25th 2019 at 02:45 AM.
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  9. #9
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    Re: Difference equation - algebra

    Just divide both side by T/Tv+1 and do some smart calculation, it just two step sum nothing so special in that
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