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Introduction to the Lagrange Interpolator Filter

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.

 



TASSART Stephan
Sat Apr 6 13:58:45 EET DST 1996