To obtain a causal FIR filter, we will expand in powers of instead of . For simplicity of notation, define . Then we obtain the Taylor series expansion of about to be
where the derivatives are with respect to , e.g., . Our maximally flat th-order Langrange FIR interpolation filter is obtain by truncating this expansion at order :
This can be viewed as an FIR filter structure in which the usual delay elements are replaced by .