Overview

This theoretical chapter examines core ideas for the whole book, the ideas of linear systems, vector spaces and functional representation. All the sensory modalities sample the incoming signal in some way, producing a discrete representation. They then transform and split this signal up into streams. Along the way the data is usually compressed. This chapter deals with how to sample a signal and represent it in different ways. The section on information theory (§3.9.3) then takes on the topic of compression.

One fundamental representational example is Fourier decomposition, crucial to vision and hearing. It is one of the most important and powerful ideas in the whole of engineering and communications and it is essential to understanding sensory processing. The mathematics is rather complicated, but the emphasis herein is on the ideas rather than the detailed formalism. For the interested reader, excellent books describing the mathematical content in much more detail are Linear Systems, Fourier Transforms and Optics by Gaskill (1978) and The Fourier Transform and its Applications by Bracewell (1999).

We already have an intuitive feel for these ideas. We know how somebody's voice changes if they have a cold, when they talk over the telephone; we know how pictures can be blurred by a dirty lens, or can vary in contrast from soft portraits to sharp lithographs. All these common phenonema are examples of filtering, of changing the frequency balance in a signal.