A binomial QMF – properly an orthonormal binomial quadrature mirror filter – is an orthogonal wavelet developed in 1990.

The binomial QMF bank with perfect reconstruction (PR) was designed by Ali Akansu, and published in 1990, using the family of binomial polynomials for subband decomposition of discrete-time signals.[1][2][3] Akansu and his fellow authors 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 (Daubechies wavelet). It was an extension of Akansu's prior work on Binomial coefficient and Hermite polynomials wherein he developed the Modified Hermite Transformation (MHT) in 1987.[4][5]

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.[6][7]


  1. ^ A.N. Akansu, An Efficient QMF-Wavelet Structure (Binomial-QMF Daubechies Wavelets), Proc. 1st NJIT Symposium on Wavelets, April 1990.
  2. ^ A.N. Akansu, R.A. Haddad and H. Caglar, Perfect Reconstruction Binomial QMF-Wavelet Transform, Proc. SPIE Visual Communications and Image Processing, pp. 609–618, vol. 1360, Lausanne, Sept. 1990.
  3. ^ A.N. Akansu, R.A. Haddad and H. Caglar, The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition, IEEE Trans. Signal Process., pp. 13–19, January 1993.
  4. ^ A.N. Akansu, Statistical Adaptive Transform Coding of Speech Signals. Ph.D. Thesis. Polytechnic University, 1987.
  5. ^ R.A. Haddad and A.N. Akansu, "A New Orthogonal Transform for Signal Coding," IEEE Transactions on Acoustics, Speech and Signal Processing, vol.36, no.9, pp. 1404-1411, September 1988.
  6. ^ H. Caglar and A.N. Akansu, A Generalized Parametric PR-QMF Design Technique Based on Bernstein Polynomial Approximation, IEEE Trans. Signal Process., pp. 2314–2321, July 1993.
  7. ^ O. Herrmann, On the Approximation Problem in Nonrecursive Digital Filter Design, IEEE Trans. Circuit Theory, vol CT-18, no. 3, pp. 411–413, May 1971.