1. 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.

2. Re: Difference equation - algebra

seriously?

just divide both sides by $\dfrac{T}{T_v} + 1$

3. Re: Difference equation - algebra

Yes, seriously

So this is equal if I multiply with:

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

4. 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 $\displaystyle \frac{T}{T_v+ T}$.

5. Re: Difference equation - algebra

Originally Posted by Nforce
Yes, seriously

So this is equal if I multiply with:

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

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

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

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

6. Re: Difference equation - algebra

Originally Posted by romsek
no ....
Romsek, wear a hockey helmet !

7. 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.

8. Re: Difference equation - algebra

Originally Posted by Nforce
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

9. 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