Wavelets in Closed Forms

  • Ahmed I. Zayed
  • Gilbert G. Walter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Almost all the known orthonormal wavelets, except for the Haar and Shannon wavelets, cannot be expressed in closed form. By a closed-form expression we mean a representation of the function in terms of elementary functions, such as trigonometric, exponential, or rational functions, or in terms of special functions of mathematical physics, such as gamma, Bessel, or hypergeometric functions. We outline a procedure for obtaining orthonormal wavelets, as well as nonorthogonal, but interpolating, wavelets. We then apply this procedure to specific cases and obtain a number of orthonormal wavelets and nonorthogonal, but interpolating, wavelets in closed-form expressions.


Inverse Fourier Transform Scaling Function Mother Wavelet Multiresolution Analysis Sampling Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Ahmed I. Zayed
  • Gilbert G. Walter

There are no affiliations available

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