Orthonormal binomial quadrature mirror filter (binomial-QMF) bank with perfect reconstruction (PR) was designed by Ali Akansu

Ali Akansu

Ali N. Akansu is a Turkish American scientist best known for his contributions to the theory and applications of sub-band and wavelet transforms.-Biography:Akansu received his B.S. degree from the Istanbul Technical University, Turkey, in 1980, his M.S...

, et al. published in 1990 using the family of binomial polynomials for subband decomposition of discrete-time signals

.
They also showed that these binomial-QMF filters are identical to the wavelet

Wavelet

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...

 filters designed independently by Ingrid Daubechies

Ingrid Daubechies

Ingrid Daubechies is a Belgian physicist and mathematician. She was between 2004 and 2011 the William R. Kenan Jr. Professor in the mathematics and applied mathematics departments at Princeton University. In January 2011 she moved to Duke University as a Professor in mathematics. She is the first...

 from compactly supported orthonormal wavelet transform perspective in 1988 (Daubechies wavelet

Daubechies wavelet

Named after Ingrid Daubechies, the Daubechies wavelets are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support...

). 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.

External links

• Daubechies Wavelet Filter
• 1st NJIT Symposium on Wavelets (April 30, 1990) (First Wavelets Conference in USA)