{"product_id":"a-first-course-on-wavelets-studies-in-advanced-mathematics-9780849382741","title":"A First Course on Wavelets (Studies in Advanced Mathematics)","description":"\u003cp\u003eWavelet theory had its origin in quantum field theory  signal analysis  and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets  from background math to powerful applications. The authors provide elementary methods for constructing wavelets  and illustrate several new classes of wavelets.  The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations  allowing the authors to introduce many new wavelets. Next  the idea of multiresolution analysis (MRA) is developed  and the authors include simplified presentations of previous studies  particularly for compactly supported wavelets.  Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis  compactly supported wavelets  and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets  such as low-pass filters and scaling functions  The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations  and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided  and constructions of splines wavelets are presented.  Mathematicians  engineers  physicists  and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45651892240437,"sku":"ByrdShop_0849382742","price":157.07,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780849382741.jpg?v=1781844114","url":"https:\/\/atxbooks.com\/products\/a-first-course-on-wavelets-studies-in-advanced-mathematics-9780849382741","provider":"ATX Books","version":"1.0","type":"link"}