\form#0:\[ y[n] - \sum_{k=1}^{M} a_k y[n-k] = \sum_{k=0}^{N} b_k x[n-k] \]
\form#1:\[ H(z) = \frac{\sum_{k=0}^{M} b_k z^{-k}}{1 - \sum_{k=1}^{N} a_k z^{-k}} \]
\form#2:\[ y[n] - (1-alpha) y[n-1] = alpha x[n] \]
\form#3:\[ H(z) = \frac{alpha}{1 - (1-alpha) z^{-1}} \]
\form#4:\[ H(z) = \frac{\sum_{k=0}^{N} b_k z^{-k}}{1 - \sum_{k=1}^{M} a_k z^{-k}} \]