Why model signals?

We are generally interested in manipulating signals. We may wish to synthesize signals, as modems need to do in order to be able to transmit a voice-like signal through the telephone channel. We may instead wish to analyze signals, as modems need to do in order to extract digital information from a received voice-like signal. In general, the field of communications is all about synthesizing signals with characteristics that match a channel, and then analyzing signals that have often been corrupted by the channel to extract the original information.

We may also wish to synthesize natural signals such as images or speech. The field of computer graphics puts much of its energy into synthesizing natural-looking images. Image processing includes image understanding, which involves analyzing images to determine their content. The field of signal processing includes analysis and synthesis of speech and music signals.

In order to analyze or synthesize signals, we need models of those signals. Since a signal is a function, a model of the signal is a description or a definition of the function. We will use two approaches. The first is a declarative (what is) approach. The second is an imperative (how to) approach. These two approaches are complementary. For certain problems, one is better than the other. For other problems, the situation is reversed.