How to calculate and plot the impulse response? $$y[n]-y[n-1]+0.9y[n-2]=x[n]$$
2026-04-01 12:32:48.1775046768
Z transform (transform function and impulse response)
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Hint. One has $$ Y(z)-z^{-1}Y(z)+0.9z^{-2}Y(z)=X(z) $$ giving $$ \frac{Y(z)}{X(z)}=H(z)=\frac1{1-z^{-1}+0.9z^{-2}}=1+\frac{z-0.9}{z^2-z+0.9} $$ then one may use a table of Laplace and Z transforms to conclude.