Dear all,
I am trying to transform the discrete LTI sytem E(z) into its partial
fraction expansion

E(z) = \frac,
N(z) = Mz^2 - Mz
D(z) = (1+K)z^3+(-2K-3)z^2+(K+3)z -1

M and K are const. D(z) is of 3rd order. E(z) has 3 poles, {1,1, \frac }

My approach was to find the coefficients A,B,C of the partial fraction terms: \frac{ (z-1)^2 } + \frac + \frac{ z-\frac }

However, all my attempts ended up with A = 0, B = \frac C = - \frac

This is confusing. E(z) has 3 poles, while its partial fraction expansion counts only 2. Further, E(z) is not stable, while its partial fraction expansion is conditional stable, i.e. its impulse response will remain on a constant value.

What am I doing wrong here?

Best regards, Chris

E(z) = \frac,

M and K are const. D(z) is of 3rd order. E(z) has 3 poles, {1,1, \frac }

My approach was to find the coefficients A,B,C of the partial fraction terms: \frac{ (z-1)^2 } + \frac + \frac{ z-\frac }

However, all my attempts ended up with A = 0, B = \frac C = - \frac

This is confusing. E(z) has 3 poles, while its partial fraction expansion counts only 2. Further, E(z) is not stable, while its partial fraction expansion is conditional stable, i.e. its impulse response will remain on a constant value.

What am I doing wrong here?

Best regards, Chris