Signal coding based on wavelet analysis

The article focuses on the analysis of the application of wavelet transforms in signal and image encoding. Wavelets are defined as a powerful tool in numerous technical and scientific disciplines, capable of effectively highlighting and processing signal characteristics at various levels of resolution. The article emphasizes the significance of wavelets in the encryption of images and signals, particularly regarding optimization of the encryption time and providing protection against various attacks. In today’s world, digital communication and data processing are gaining incredible importance, wavelet analysis is the key to success in numerous technical and scientific disciplines. This wavelet analysis article considers the meaning and application of wavelet analysis in signal coding. The history of wavelet analysis, its mathematical foundations, as well as modern methods and technologies that use this analysis to improve and optimize coding processes are considered. The value of wavelets in signal coding lies in their ability to efficiently extract and process signal characteristics at different levels of resolution. This versatility makes wavelets extremely useful in a wide range of applications, from image and video compression to cryptographic encryption and medical signal processing. This article examines the various ways in which wavelet transforms can improve signal coding, providing greater efficiency and security in a variety of applications, provides a deeper understanding of the role of wavelet analysis in modern signal coding. An innovative approach to encryption, which combines the Haar wavelet transform and «golden» matrices, opens up new possibilities in the cryptographic protection of digital signals. The article considers various approaches to the selection and application of wavelets for specific signal processing tasks, emphasizing their mathematical properties and practical effectiveness. The value of wavelets in the encryption of images and signals is reflected in the need to optimize encryption time and ensure protection against various attacks. Modern methods of wavelet coding need additional improvement to solve the task of processing different types of signals taking into account noise, frequency changes and other complexities.