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$$
H(z)={\frac  {Y(z)}{X(z)}}={\frac  {\sum _{{q=0}}^{{M}}z^{{-q}}\beta _{{q}}}{\sum _{{p=0}}^{{N}}z^{{-p}}\alpha _{{p}}}}={\frac  {\beta _{0}+z^{{-1}}\beta _{1}+z^{{-2}}\beta _{2}+...+z^{{-M}}\beta _{M}}{\alpha _{0}+z^{{-1}}\alpha _{1}+z^{{-2}}\alpha _{2}+...+z^{{-N}}\alpha _{N}}}\ 
$$
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