From the partial series expansion of 
we derive a family of
FIR filters
whose transfer function 
is defined in eq. (3)
by replacing x by 
in eq. (2):
From the convergence disk of the power series expansion, we deduce
that the family of filters converges at low frequency (i.e. 
), but we will see in the following sections that this
limit is usually not a key point. The transfer functions
may also be recast as a nested expression corresponding to the Horner
scheme (eq. 4).
