Vol.13, No.1, February 2024.                                                                                                                                                                               ISSN: 2217-8309

                                                                                                                                                                                                                        eISSN: 2217-8333


TEM Journal



Association for Information Communication Technology Education and Science

Application of Discrete and Fast Fourier Transforms to Increase the Speed of Multiscale Image Analysis


Viliam Ďuriš, Vladimir I. Semenov, Sergey G. Chumarov


© 2024 Viliam Ďuriš, published by UIKTEN. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. (CC BY-NC-ND 4.0)


Citation Information: TEM Journal. Volume 13, Issue 1, Pages 349-354, ISSN 2217-8309, DOI: 10.18421/TEM131-36, February 2024.


Received: 23 September 2023.

Revised:   03 January 2024.
Accepted: 18 January 2024.
Published: 27 February 2024.




The paper compares the accuracy of reconstruction using different wavelets, and the authors also use fast and discrete Fourier transforms together to calculate the forward and inverse continuous wavelet transform in the frequency domain. Due to the use of calculations in the frequency domain, it becomes possible to perform decomposition, reconstruction, image filtering, and other transformations with high performance and precision. For multiscale signal analysis, a wavelet with a rectangular amplitude-frequency response has been constructed, which allows for an increase in the accuracy of decomposition and reconstruction compared to the Mallat algorithm presented in Matlab computer mathematics. At the same time, the time of multiscale analysis is reduced several times compared to the Mallat algorithm.


Keywords –Discrete fourier transform (DFT), fast fourier transform (FFT), fast wavelet transform (FWT), frequency domain, Mallat algorithm.



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