The LIF of order N consists in a FIR filter, 
, where 
are parametrised by a
polynomial in d. The LIF has to correspond to an exact delay filter
when d is integer, which means that 
for k
between 0 and N. This leads to a system of linear equations whose
solution gives the impulse response (see [2]):
As pointed out in [4], it appears that any filter which verifies the so called maximally flat condition (eq. 3) is a LIF. Said differently it means that the LIF corresponds to the FIR filter whose Fourier transform best fits the ideal Fourier transform at the zero frequency.
