The Lagrange Interpolator Filter (LIF) of order N consists in a FIR
filter, 
, whose
coefficients 
are polynomial in d. By definition, the
LIF corresponds to an exact delay filter when d is an integer, which
means that 
must equal 
for each k between 0 and
N. This leads to a system of linear equations whose solution is
given in [Laakso et al., 1996]:
As pointed out in [Hermanowicz, 1992], it appears that any filter which verifies the so called maximally flat condition (eq. (2)) is also a LIF. Said differently, it means that the LIF corresponds to the FIR filter whose Fourier transform best fits the ideal Fourier transform for a frequency of zero.
