# How to find the difference equation from system response or primitive equation?

If I have a system response or the primitive equation , how can i find its difference equation by mathematica?

eg:

h[n] = b0 a^n u[n] + b1 a^n-1 u[n-1]
H[z] = b0 + b1 z^-1 / (1- a z^-1), |z| > |a|


expect:

y[n] - a y[n-1] = b0 x[n] + b1 x[n-1]

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• Please try to be a bit clearer in your example. This will help others in understanding and solving your problem Mar 1 at 5:10

tfm = TransferFunctionModel[(b0 + b1 z^-1)/(1 - a z^-1), 1/z, SamplingPeriod -> 1];
ControlDEqnsioEqnsForm[tfm][[1, 1]] 