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ARMA model/IIR filter in state space
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[QUOTE="divB, post: 4520365, member: 229997"] Hi Thanks, that's a really great explanation! I fully understand how I obtain the second equation, y(n)=c^Tx+du, from the initially given difference equation. And I think I can see that for the case of a AR-only or MA-only system the transition matrix is just the identity matrix. Please correct me if I am already wrong here: MA case: [tex] y(k) = [ a_1 , \cdots a_r ] x + 1 u(k) \\ x(k) = [u(k-1) , u(k-2), \cdots, u(k-r) ]^T \\ x(k+1) = I\cdot x(k) [/tex] Similarly for the AR case where [tex] y(k) = [ b_1 , \cdots b_p ] x + 1 u(k) \\ x(k) = [y(k-1) , y(k-2), \cdots, y(k-p) ]^T \\ x(k+1) = I\cdot x(k) [/tex] However, I am stuck when I have both of them. I think I would do the same having an (r+p)-length state vector. However, intuition tells me, that a max{p,r}-length state vector should suffice. (BTW: I know that there are many solutions and the (r+p) variant might work) I tried using [itex]x_1(k) = b_1y(n-1) + a_1 u(n-1)[/itex] etc. as state vector. However, in this case it seems to be impossible to find a matching transition matrix. I think I still do not see how the "receipt" how I can transform any such differential/difference equation to state space :-( I guess the first step is always using the difference equation and transforming the y(k)= equation into the the y=c^t x + du equation. Is this commonly right? Or is even there a difference, based on which state vector I choose? Thanks again, divB [/QUOTE]
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ARMA model/IIR filter in state space
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