Using partial fraction decomposition method, obtain the inverse z-transform of the transfer function $H(z)$ given below, and calculate the $h[n]$ impulse response that corresponds to a causal discrete-time system.\\ $H(z) = \frac{z(z+2)}{(z-0.2)(z+0.6)} = \frac{1+2z^{-1}}{(1-0.2z^{-1})(1+0.6z^{-1})}$

          Using partial fraction decomposition method, obtain the inverse z-transform of the transfer function $H(z)$ given below, and calculate the $h[n]$ impulse response that corresponds to a causal discrete-time system.\\
$H(z) = \frac{z(z+2)}{(z-0.2)(z+0.6)} = \frac{1+2z^{-1}}{(1-0.2z^{-1})(1+0.6z^{-1})}$

$Using partial fraction decomposition method, obtain the inverse z-transform of the transfer function H(z) given below, and calculate the h[n] impulse response that corresponds to a causal discrete-time system. H(z) = (z(z+2))/((z-0.2)(z+0.6)) = (1+2z^-1)/((1-0.2z^-1)(1+0.6z^-1))$

Added by Lorena C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

09/16/2023

Step 1

The denominator of H(z) is (1-0.2z^(-1))(1+0.6z^(-1))(z-0.2)(z+0.6). To factorize this, we can write it as: (1-0.2z^(-1))(1+0.6z^(-1))(z-0.2)(z+0.6) = A/(1-0.2z^(-1)) + B/(1+0.6z^(-1)) + C/(z-0.2) + D/(z+0.6) where A, B, C, and D are constants that we need to Show more…

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Using partial fraction decomposition method, obtain the inverse z-transform of the transfer function.H(z) given below, and calculate the h[n] impulse response that corresponds to a causal discrete-time system. z(z+2) 1+2 z-1 H(z)= z-0.2)(z+0.6) (1-0.2 z-1)(1+0.6 z-1)