Wavelets in Closed Forms
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.
KeywordsInverse Fourier Transform Scaling Function Mother Wavelet Multiresolution Analysis Sampling Function
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