University of Isfahan Mathematics and Society 2345-6493 4 1 2019 05 22 Wavelets' applications in signal processing Wavelets' applications in signal processing 29 36 24022 10.22108/msci.2019.118249.1331 FA Hojatollah Saeidi Applied Mathematics, Faculty of Mathematics, Shahrekord University, Iran Zohre Saeidi Electrical Engineering, Faculty of Technology, Shahrekord University, Iran Journal Article 2019 07 18 Wavelets are powerful tools for decomposition, analysis, and processing of digital signals. The wavelet transform represents the time-domain of a signal in terms of wavelet coefficients, converting it into a frequency-time representation. Wavelet coefficients can be utilized as part of a frequency-dependent method to achieve various signal processing effects. Additionally, the inverse wavelet transform converts the obtained wavelet coefficients back into the time-domain representation to obtain a modified signal. In this article, after a brief overview of the Fourier method and wavelet transform, the Haar wavelet and Daubechies wavelet are described. Following that, several signal processing techniques using wavelets, including noise reduction, wavelet denoising, data compression, musical effects, and a Java-based wavelet processor, will be examined. Wavelets are powerful tools for decomposition, analysis, and processing of digital signals. The wavelet transform represents the time-domain of a signal in terms of wavelet coefficients, converting it into a frequency-time representation. Wavelet coefficients can be utilized as part of a frequency-dependent method to achieve various signal processing effects. Additionally, the inverse wavelet transform converts the obtained wavelet coefficients back into the time-domain representation to obtain a modified signal. In this article, after a brief overview of the Fourier method and wavelet transform, the Haar wavelet and Daubechies wavelet are described. Following that, several signal processing techniques using wavelets, including noise reduction, wavelet denoising, data compression, musical effects, and a Java-based wavelet processor, will be examined. https://math-sci.ui.ac.ir/article_24022_bf3ca2e79c1c5ae6262ec68b7b409572.pdf