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• W2078457119 endingPage "2111" @default.
• W2078457119 startingPage "2111" @default.
• W2078457119 abstract "We prove several theorems and construct explicitly the bridge between the continuous and discrete adaptive wavelet transform (AWT). The computational efficiency of the AWT is a result of its compact support closely matching linearly the signal's time-frequency characteristics, and is also a result of a larger redundancy factor of the superposition-mother s(x) (super-mother), created adaptively by a linear superposition of other admissible mother wavelets. The super-mother always forms a complete basis, but is usually associated with a higher redundancy number than its constituent complete orthonormal (CON) bases. The robustness of super-mother suffers less noise contamination (since noise is everywhere, and a redundant sampling by bandpassings can suppress the noise and enhance the signal). Since the continuous super-mother has been created off-line by AWT (using least-mean-squares neural nets), we wish to accomplish fast AWT on line. Thus, we formulate AWT in discrete high-pass (<i>H</i>) and low-pass (<i>L</i>) filter bank coefficients via the quadrature mirror filter (QMF), a digital subband lossless coding. A linear combination of two special cases of the complete biorthogonal normalized (Cbi-ON) QMF [<i>L</i>(<i>z</i>),<i>H</i>(<i>z</i>),<i>L⁺</i>(<i>z</i>),<i>H</i>⁺(<i>z</i>)], called α-bank and β-bank, becomes a hybrid <i>a</i>α + <i>b</i>β-bank (for any real positive constants <i>a</i> and <i>b</i>) that is still admissible, meaning Cbi-ON and lossless. Finally, the power of AWT is the implementation by means of wavelet chips and neurochips, in which each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling." @default.
• W2078457119 created "2016-06-24" @default.
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• W2078457119 date "1994-07-01" @default.
• W2078457119 modified "2023-09-26" @default.
• W2078457119 title "Mathematics of adaptive wavelet transforms: relating continuous with discrete transforms" @default.
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• W2078457119 doi "https://doi.org/10.1117/12.173205" @default.
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