What is the algebraic signal processing theory?
• What is the scope of the algebraic theory? • What does the algebraic theory enable me to do that I could not do before? • How accessible is the algebraic theory (how much math do I need)? What is the algebraic signal processing theory? The algebraic signal processing theory is a new approach to and an extension of linear signal processing (henceforth called SP), that is, SP built around the concepts of filters, spectrum, Fourier transform, and others. The theory provides a general framework of signals, filtering, z-transform, Fourier transforms, etcetera. Well-known and new ways of doing SP are instantiations of this framework. Examples of instantiations include discrete infinite and finite time and discrete infinite and finite space in one and higher dimensions, separable and non-separable. A glimpse is shown in the table. In the left column is the generic theory, the four right columns are instantiations. Note that every instantiation has a “z-transform.” Also note that the discret
