Mathematical Preliminary
Jaideva C. Goswami, Andrew K. Chan · 2010
The purpose of this chapter is to familiarize the reader with some of the mathematical notations and tools that are useful in an understanding of wavelet theory. For a more detailed discussion of functional spaces, the reader is referred to standard texts on real analysis. A fundamental understanding of topics in digital signal processing, such as sampling, the z - transform, linear shift - invariant systems, and discrete convolution, are necessary for a good grasp of wavelet theory. In addition, a brief discussion of linear algebra and matrix manipulations is included that is very useful in discrete - time domain analysis of filter banks. Biorthogonal representation is a possible alternative to overcoming the constraint in orthogonality and producing a good approximation to a given function. The Shannon basis is an example of a Riesz basis that is orthonormal, since the spectrum of the Shannon function is one in the interval. Controlled Vocabulary Terms digital signal processing; digital signals; information theory; matrix algebra