ABSTRACT
The most important tool in the construction of wavelet theory is Fourier ana lysis. The subsequent chapters rely on many of the well-known theorems and formulas relating to Fourier series, as well as on a basic understanding of the Fourier transform on R. These ideas will be presented in the following sections in the way of a review, so that they can readily be used later on. For the cor responding proofs we refer the reader to the pertinent textbooks, e.g., [2], [5], [10], [15]. In Sections 2.3 and 2.4 we give an account of the Heisenberg uncer tainty principle and of the Shannon sampling theorem. These two theorems point to certain definitive limits of signal theory, and, in consequence, they also also play a decisive, if sometimes hidden, role in all work with wavelets.
