Geodesic
Evaluation of a continuous wavelet transform by solving the Cauchy problem for a system of partial differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 77-82

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It is shown that the problem of evaluating the continuous Morlet wavelet transform can be stated as the Cauchy problem for a system of two partial differential equations. The initial conditions for the desired functions, i.e., for the real and imaginary parts of the wavelet transform, are the analyzed function and a vanishing function, respectively. Numerical examples are given. 
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     author = {E. B. Postnikov},
     title = {Evaluation of a~continuous wavelet transform by solving the {Cauchy} problem for a~system of partial differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {77--82},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a7/}
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E. B. Postnikov. Evaluation of a continuous wavelet transform by solving the Cauchy problem for a system of partial differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 77-82. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_1_a7/