Location:Training / Embedded Development / DSP / Wavelets and science / Orthogonal direct sum decomposition of function space and complete wavelet subspace decomposition

Wavelet is a novel scientific idea and method that has been rapidly developed and increasingly perfected since its emergence in the 1980s. It is the selfless contribution of many scientists and engineers in the contemporary mainstream scientific research field to exhaust their outstanding wisdom and contribute to the treasure house of human thoughts and cognitive methods. A majestic scientific symphony chapter. The wavelet method has localization capabilities in both the observation domain and the transformation domain. Its wide application has promoted mathematics, physics, computer science, optics, acoustics, biology and medicine, information science, control science, visual science, quantum theory, Scientific concepts and ideas, epistemology and calculation methods in the main frontier fields of contemporary science and technology, including astrophysics, management, precision mechanics and aerospace science, have entered a new era, with fruitful results and large-scale innovations achieved. Wavelet theory also enjoys the reputation of "mathematical microscope".
The course "Wavelets and Science" is aimed at college students, graduate students and scientific researchers who are in their second year of study in science, engineering, management, medicine and other disciplines and have experience in learning linear algebra and calculus. It plans to introduce the wavelet method to solve contemporary problems through 24 hours of study. Typical successful cases of research issues in mainstream frontier fields of science and technology, helping learners understand and master the scientific ideas and research methods of the core wavelet theory, such as wavelets, wavelet multi-resolution analysis, wavelet packets, wavelets and wavelet packet decomposition/synthesis algorithms, etc. Establish new thinking to understand typical cutting-edge issues in contemporary science based on wavelet thought, and cultivate and improve learners' innovative research capabilities in using wavelet methods and theories to solve scientific and technological problems.
The main content of the course "Wavelets and Science" includes a brief history of wavelets, basic properties of wavelets and wavelet transforms, wavelet multi-resolution analysis methods, wavelet construction and examples, wavelet packet theory, wavelets and time-frequency localization of wavelet packets, wavelet and wavelet packet decomposition/synthesis algorithm, image wavelet transform and wavelet packet transform, image wavelet and wavelet packet pyramid algorithm, wavelet application topics: wavelet packets and uncertainty principle, wavelet and signal filtering and image filtering, wavelet application topics : Wavelet and image compression, etc.