Orthonormal Binomial Quadrature Mirror Filter (Binomial-QMF) bank with perfect reconstruction (PR) was designed by Ali Akansu
, et.al. in 1990 using discrete-time Binomial polynomials. They also showed that these Binomial-QMF filters are identical to the Wavelet
Filters designed independently by Ingrid Daubechies
from compactly supported orthonormal wavelet transform perspective in 1988. Later, it was shown that the magnitude square functions of low-pass and high-pass Binomial-QMF filters are the unique maximally flat functions in a two-band PR-QMF design framework.